Tootfinder

Symmetric Spaces with Rectangular Unit Lattices, Revisited
Jost-Hinrich Eschenburg, Ernst Heintze, Peter Quast
https://arxiv.org/abs/2509.16166 https://arx…

Symmetric Spaces with Rectangular Unit Lattices, Revisited
We give a new proof of a theorem of Loos stating that a Riemannian symmetric space X with rectangular unit lattice is a symmetric R-space. For this we construct explicitly an isometric extrinsically symmetric embedding of X in a Euclidean space which reveals X as a standardly embedded symmetric R-space. We further determine the root systems, Euclidean root data, fundamental groups and eigenvalues of the Laplacian of symmetric spaces with rectangular unit lattice in a direct way.

Scalar induced gravitational waves in PV symmetric teleparallel gravity with non-minimally coupled boundary term
Fengge Zhang
https://arxiv.org/abs/2508.14584 https://

Scalar induced gravitational waves in PV symmetric teleparallel gravity with non-minimally coupled boundary term
The question of whether the parity violation occurs in gravitational interaction has recently attracted much attention. In this paper, we investigate the scalar induced gravitational waves (SIGWs) in symmetric teleparallel gravity incorporating a parity-violating (PV) term and a non-minimally coupled boundary term. The presence of this non-minimally coupled boundary term help to avoid the strong coupling problem inherent in PV symmetric teleparallel gravity, thereby enabling our study of the SI…

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family
Jacek Karwowski, Frank Nielsen
https://arxiv.org/abs/2508.14369

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family
The extended Gaussian family is the closure of the Gaussian family obtained by completing the Gaussian family with the counterpart elements induced by degenerate covariance or degenerate precision matrices, or a mix of both degeneracies. The parameter space of the extended Gaussian family forms a symmetric positive semi-definite matrix bicone, i.e. two partial symmetric positive semi-definite matrix cones joined at their bases. In this paper, we study the Hilbert geometry of such an open bounde…

Multi-virtual braid groups
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Komal Negi, Madeti Prabhakar
https://arxiv.org/abs/2507.14551 https://

Multi-virtual braid groups
L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and multi-virtual semi-pure braid groups, which are normal subgroups of index $n!$. We give a set of generators and defining relations for these groups, show that multi-virtual (symmetric multi-virtual) braid group is a semi-direct products of multi-virtual pure (symmetric multi-virtual pure) braid group and symmetric group. …

Symmetric powers of $S^{(n-1,1)}$ and $D^{(n-1,1)}$
Pavel Turek, Jialin Wang
https://arxiv.org/abs/2507.15505 https://arxiv.org/pdf/2…

Symmetric powers of $S^{(n-1,1)}$ and $D^{(n-1,1)}$
Let $p$ be a prime and $n\geq 2$ be a positive integer. We establish new formulae for the decompositions of the first $p-1$ symmetric powers of the Specht module $S^{(n-1,1)}$ and the irreducible module $D^{(n-1,1)}$ in characteristic $p$ as direct sums of Young permutation modules. As an application of the formulae, we show that these symmetric powers have Specht filtration and find the vertices of their indecomposable summands. Our main tool, constructed in this paper, is a lift of a splittin…

Massive spin 3 and Metric-Affine Gravity
Roberto Percacci, Ergin Sezgin
https://arxiv.org/abs/2508.14211 https://arxiv.org/pdf/2508.14211

Massive spin 3 and Metric-Affine Gravity
Symmetric Metric-Affine Gravity is a theory of gravity with an independent non-metric connection, and zero torsion. It can be thought of as ordinary metric gravity coupled to a rank-three tensor Q, symmetric in one pair of indices. This field carries a spin-three degree of freedom. We find that, in contrast to the totally symmetric case, it is possible to arrange the parameters in the Lagrangian, so that, at the linearized level, the spin-three state, either alone or in combination with a spin-…

Sub-GeV Sterile Neutrino as a Probe of Neutrino Mass Generation in the Minimal Left-Right Symmetric Model
Gang Li, Ying-Ying Li, Sida Lu, Ye-Ling Zhou
https://arxiv.org/abs/2508.15609

Sub-GeV Sterile Neutrino as a Probe of Neutrino Mass Generation in the Minimal Left-Right Symmetric Model
The minimal left-right symmetric model (mLRSM) provides an elegant and testable framework for addressing the origin of neutrino masses. We examine the constraints on the sub-GeV sterile neutrino in the type-II seesaw scenario of the mLRSM without left-right mixing, taking limits from collider searches, meson decays, supernovae, neutrinoless double beta ($0νββ$) decay and cosmology. Specifically, we derive the $0νββ$ decay constraints using the advanced effective field theory approach and …

A Note on the Convergence of Symmetric Triangle Quadrature Rules
Brian A. Freno, Neil R. Matula, Joseph E. Bishop
https://arxiv.org/abs/2508.15133 https://…

A Note on the Convergence of Symmetric Triangle Quadrature Rules
Symmetric polynomial quadrature rules for triangles are commonly used to efficiently integrate two-dimensional domains in finite-element-type problems. While the development of such rules focuses on the maximum degree a given number of points can exactly integrate, smooth integrands are generally not polynomials of finite degree. Therefore, for such integrands, one needs to balance integration accuracy and computational cost. A natural approach to this balance is to choose the number of points …

Invertible exterior powers
Kevin Coulembier
https://arxiv.org/abs/2507.14803 https://arxiv.org/pdf/2507.14803

Invertible exterior powers
We show that in a symmetric monoidal category over a field of characteristic zero, objects with an invertible exterior power are rigid. As an application we prove some conjectures on dimensions in symmetric monoidal categories recently stated by Baez, Moeller and Trimble.

Global Spherically Symmetric Solutions and Relaxation Limit for the Relaxed Compressible Navier-Stokes Equations
Yuxi Hu, Mengran Yuan
https://arxiv.org/abs/2507.15179

Global Spherically Symmetric Solutions and Relaxation Limit for the Relaxed Compressible Navier-Stokes Equations
This paper studies an initial boundary value problem for the multidimensional hyperbolized compressible Navier-Stokes equations, in which the classical Newtonian law is replaced by the Maxwell law. We seek spherically symmetric solutions to the studied system in an exterior domain of a ball in $\mathbb R^3$, which are a system possessing a uniform characteristic boundary. First, we construct an approximate system featuring a non-characteristic boundary and establish its local well-posedness. Su…

Co-periods and central symmetric cube L-values
Cai Li, Fan Yangyu, She Dongming
https://arxiv.org/abs/2507.15279 https://arxiv.org/pd…

Co-periods and central symmetric cube L-values
In this article, we study the co-period integral attached to an automorphic form on $\GL(2)$ and two exceptional theta series on the cubic Kazhdan-Patterson cover of $\GL(2)$. In the local aspect, we show the $\Hom$-space is always of one dimension and conduct the unramified calculations. In the global aspect, we give the Euler decomposition for the co-period integrals of Eisenstein series and propose an Ichino-Ikeda type conjecture relating the co-period integrals of cuspidal forms to the cent…

The fundamental module of $S_3$-symmetric tridiagonal algebra associated with cycles
J. V. S. Morales
https://arxiv.org/abs/2508.13540 https://arxiv.org/pd…

The fundamental module of $S_3$-symmetric tridiagonal algebra associated with cycles
Terwilliger recently introduced the $S_3$-symmetric tridiagonal algebra, a generalization of the tridiagonal algebra. This algebra has six generators naturally associated with the vertices of a regular hexagon: adjacent generators satisfy the tridiagonal relations, while non-adjacent ones commute. To each $Q$-polynomial distance-regular graph $Γ$, we associate scalars $β, γ, γ^*, \varrho, \varrho^*$, and define the corresponding $S_3$-symmetric tridiagonal algebra $\mathbb{T} = \mathbb{T}(Î…

On the asymptotic equidistribution of word values in symmetric groups
Vadim Alekseev, Jakob Schneider, Andreas Thom
https://arxiv.org/abs/2507.13928 https:…

On the asymptotic equidistribution of word values in symmetric groups
We prove an asymptotic equidistribution result for word values for words with constants in the symmetric group. We also speculate about simultaneous asymptotic equidistribution results for values of $d$-tuples of elements of $\mathbb F_d$.

Symmetric and non-symmetric F-conjectures are equivalent
Maksym Fedorchuk, Anton Mellit
https://arxiv.org/abs/2507.12434 https://arxi…

Symmetric and non-symmetric F-conjectures are equivalent
The F-conjecture gives a conjectural description of the ample cone of the Deligne-Mumford moduli space $\overline{M}_{g,n}$. We prove that the $S_n$-symmetric and the non-symmetric F-conjectures are equivalent. We also prove the Strong F-conjecture for $\overline{M}_{0,8}$ (and give an alternative proof for $\overline{M}_{0,7})$. Finally, we derive, as a consequence, the F-conjecture for the moduli space of stable curves $\overline{M}_{g}$ up to genus $g\leq 44$.

Symmetric orthogonalization and probabilistic weights in resource quantification
G\"okhan Torun
https://arxiv.org/abs/2508.12949 https://arxiv.org/pdf…

Symmetric orthogonalization and probabilistic weights in resource quantification
Transforming non-orthogonal bases into orthogonal ones often sacrifices essential properties or physical meaning in quantum systems. Here, we demonstrate that Löwdin symmetric orthogonalization (LSO) outperforms the widely used Gram-Schmidt orthogonalization (GSO) in characterizing and quantifying quantum resources, with particular emphasis on coherence and superposition. We employ LSO both to construct an orthogonal basis from a non-orthogonal one and to obtain a non-orthogonal basis from an …

Skew-symmetric super-biderivations of the special Lie superalgebra S(m, n; t)
Da Xu, Xiaoning Xu
https://arxiv.org/abs/2508.12064 https://arxiv.org/pdf/250…

Skew-symmetric super-biderivations of the special Lie superalgebra S(m, n; t)
This paper aims to study the skew-symmetric super-biderivations of the special Lie superalgebra S(m, n; t). Let S denote the special Lie superalgebra S(m, n; t) over a field of characteristic p > 2.Utilizing the abelian subalgebra TS and the weight space decomposition of S with respect to TS ,we show the action of a skew-symmetric super-biderivation on the elements of TS and some specific elements of S. Moreover, we prove that all skew-symmetric super-biderivations of S are inner.

An explicit construction of the Weyl module as a quotient of symmetric tensors by dual Garnir relations
Eoghan McDowell
https://arxiv.org/abs/2508.14788 https://

An explicit construction of the Weyl module as a quotient of symmetric tensors by dual Garnir relations
The Weyl modules are the standard modules for the Schur algebra. Their duals (the costandard modules) have well-known constructions as quotients of exterior powers and as submodules of symmetric powers. This paper presents analogous constructions for the Weyl modules themselves, introducing relations that are a non-trivial dualisation of the Garnir relations. More generally, our constructions describe endofunctors on the category of representations of any group.

Coherence for Pseudo Commutative Monads
Diego Manco
https://arxiv.org/abs/2509.15101 https://arxiv.org/pdf/2509.15101…

Coherence for Pseudo Commutative Monads
We prove that the free algebra functor associated to a symmetric, pseudo commutative 2-monad, from the underlying symmetric monoidal 2-category to the 2-category of algebras and pseudo maps over the 2-monad can be enhanced to a multifunctor. Furthermore, we prove that this multifunctor is pseudo symmetric. Our proof implies coherence results for both symmetric and non-symmetric pseudo commutative 2-monads conjectured by Hyland and Power.

On the Impossibility of Obtaining Time-Independent, Three-Dimensional, Spherically-Symmetric Densities of Confined Systems of Relativistically Moving Constituents
Gerald A. Miller
https://arxiv.org/abs/2507.14388

On the Impossibility of Obtaining Time-Independent, Three-Dimensional, Spherically-Symmetric Densities of Confined Systems of Relativistically Moving Constituents
The quantum mechanical definition of probability, the uncertainty principle and Poincare invariance provide strong basic restrictions on the ability to define spatial densities associated with form factors describing the properties of confined systems of relativistically moving constituents. Despite this, many papers ignore one or more of these restrictions. Here I show how to obtain time-independent, two-dimensional densities that are consistent with the stated restrictions. This is done using…

Any-Dimensional Polynomial Optimization via de Finetti Theorems
Eitan Levin, Venkat Chandrasekaran
https://arxiv.org/abs/2507.15632 https://

Any-Dimensional Polynomial Optimization via de Finetti Theorems
Polynomial optimization problems often arise in sequences indexed by dimension, and it is of interest to produce bounds on the optimal values of all problems in the sequence. Examples include certifying inequalities between symmetric functions or graph homomorphism densities that hold over vectors and graphs of all sizes, and computing the value of mean-field games viewed as limits of games with a growing number of players. In this paper, we study such any-dimensional polynomial problems using …

Idefix-Closed Languages and Their Application in Contextual Grammars
Marvin K\"odding, Bianca Truthe
https://arxiv.org/abs/2507.15312 https://arxiv.or…

Idefix-Closed Languages and Their Application in Contextual Grammars
In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate infix-, prefix-, and suffix-closed languages (referred to as idefix-closed languages) and compare such language families to some other subregular families of languages (finite, monoidal, nilpotent, combinational, (symmetric) definite, ordered, non-counting, power-separating, commutative, circular, union-free, star, and comet …

On the quantum algebra $su_q(1,1)$ from a Special Function standpoint
R. Alvarez-Nodarse, A. Arenas-Gomez
https://arxiv.org/abs/2507.14100 https://

On the quantum algebra $su_q(1,1)$ from a Special Function standpoint
In this paper, we study the tensor product of two unitary irreducible representations, as well as the tensor product of a unitary irreducible representation with a finite-dimensional one, and determine the corresponding Clebsch-Gordan coefficients. Using von Neumann's projection operator method, we obtain an explicit representation of these coefficients, which allows us to express them as symmetric q-hypergeometric series. Finally, by leveraging the properties of the q-hypergeometric function, …

On global regular axially-symmetric solution to the Navier-Stokes equations in a cylinder
Wies{\l}aw J. Grygierzec, Wojciech M. Zaj\k{a}czkowski
https://arxiv.org/abs/2507.14964

On global regular axially-symmetric solution to the Navier-Stokes equations in a cylinder
We consider the axisymmetric Navier-Stokes equations in a finite cylinder $Ω\subset\mathbb{R}^3$. We assume that $v_r$, $v_φ$, $ω_φ$ vanish on the lateral part of boundary $\partialΩ$ of the cylinder, and that $v_z$, $ω_φ$, $\partial_zv_φ$ vanish on the top and bottom parts of the boundary $\partialΩ$, where we used standard cylindrical coordinates, and we denoted by $ω={\rm curl}\, v$ the vorticity field. We use $H^3$ Sobolev estimates for the modified stream function (stream functio…

Why Do We See So Few Black Holes in Massive Binaries?
S. Karpov, V. Lipunov
https://arxiv.org/abs/2509.15977 https://arxiv.org/pdf/2509.15977

Why Do We See So Few Black Holes in Massive Binaries?
We offer a simple explanation for the small number of black holes observed in pairs with massive stars. In detached massive binaries, spherically symmetric accretion takes place. This accretion could result in effective energy release in the hard band only if the equipartition of the gravitational and magnetic energy of plasma is established (Shvartsmans theorem). However, we show that due to the magnetic exhaust effect this equilibrium is virtually never established for the actual magnetic fie…

Pseudorandomness of Expander Walks via Fourier Analysis on Groups
Fernando Granha Jeronimo, Tushant Mittal, Sourya Roy
https://arxiv.org/abs/2507.14445 htt…

Pseudorandomness of Expander Walks via Fourier Analysis on Groups
One approach to study the pseudorandomness properties of walks on expander graphs is to label the vertices of an expander with elements from an alphabet $Σ$, and study the mean of functions over $Σ^n$. We say expander walks $\varepsilon$-fool a function if, for any unbiased labeling of the vertices, the expander walk mean is $\varepsilon$-close to the true mean. We show that: - The class of symmetric functions is $O(|Σ|\cdotλ)$-fooled by expander walks over any generic $λ$-expa…

A large color $R$-matrix for $\mathfrak{sl}_3$
Angus Gruen, Lara San Mart\'in Su\'arez
https://arxiv.org/abs/2508.15171 https://arxiv.org/pdf/2508.…

A large color $R$-matrix for $\mathfrak{sl}_3$
We construct the invariant $F_K^{\mathfrak{sl}_3}\in\mathbb{Z}[q,q^{-1}][[x,y]]$ for any positive braid knot $K$, whose existence was conjectured by Park, building on earlier work of Gukov--Manolescu. The main step in our work extends a result by the first author on the invariant associated to symmetric representations of $\mathfrak{sl}_3$ to all irreducible representations. We conclude with a conjectural framework for constructing $F_K^{\mathfrak{sl}_N}$ for arbitrary $N$.

A Quantum Analogue of the Pfaffian-Determinant Identity, An Algebraic and Geometric Study in the q-Skew-Symmetric Case
Hani Safadi
https://arxiv.org/abs/2508.11634 https://

A Quantum Analogue of the Pfaffian-Determinant Identity, An Algebraic and Geometric Study in the q-Skew-Symmetric Case
This paper explores a quantum deformation of the classical identity Pf(A)^2 = det(A) for 2n by 2n skew-symmetric matrices A, which classically relates the square of the Pfaffian to the determinant. In the quantum setting, we study matrices whose entries lie in a noncommutative algebra and satisfy the q-skew-symmetry relations a_ji = -q times a_ij and a_ii = 0, where q is a nonzero complex parameter. This deformation introduces new algebraic structures and challenges in defining quantum analogue…

Geometry-Driven Lattice of Photonic Spin-Meron Tubes in Free Space
Anand Hegde, Komal Gupta, Yanan Dai, Chen-Bin Huang
https://arxiv.org/abs/2508.14450 https://

Geometry-Driven Lattice of Photonic Spin-Meron Tubes in Free Space
We theoretically demonstrate the first photonic spin-meron tube lattice in free space using spin-angular momentum vectors. Square-block diffraction creates $C_{4}$-symmetric beams with $π/2$ phase steps. Non-paraxial spin-orbit coupling then forms finite-length meron tubes ($N_{\mathrm{sk}} \approx \pm 1/2$, $> 25,λ$). Extending the formalism, we show that $C_{3}$ geometry of a triangular block yields a spin-skyrmion tube. Stratton-Chu theory and full-vectorial finite-difference time-domain c…

Transport evidence of current-induced nematic Dirac valleys in a parity-time-symmetric antiferromagnet
H. Sakai, Y. Miyamoto, M. Kimata, H. Watanabe, Y. Yanase, M. Ochi, M. Kondo, H. Murakawa, N. Hanasaki
https://arxiv.org/abs/2508.12397

Transport evidence of current-induced nematic Dirac valleys in a parity-time-symmetric antiferromagnet
Itinerant antiferromagnets with broken time-reversal symmetry have recently attracted attention, since their spin-split bands enable large magnetotransport responses comparable to ferromagnets despite the negligible spontaneous magnetisation. When the inversion symmetry is further broken by the antiferromagnetic order, the emerging odd-parity multipole order renders the bands spin-degenerate but asymmetric in the momentum space. For such parity-time-symmetric antiferromagnets, it has been predi…

Particle detection among Random Walks as a non-reversible Random Interlacements Process
Gonzalo Panizo, Carlos Mart\'inez
https://arxiv.org/abs/2507.14816

Particle detection among Random Walks as a non-reversible Random Interlacements Process
Consider the random set composed of particles initially distributed on Zd, d >= 2, according to a Poisson point process of intensity u > 0 and moving as independent simple symmetric random walks, the trap particles. We are interested in the detection by these particles of a target particle, initially at the origin and able to move with finite mean speed. The escape strategy for the target particle is to stay inside the infinite cluster of empty sites, assuming u is in the subcritical site perco…

Eigenvalue distribution of some random matrices
Jebalia Mohamed, Ahmed Souabni
https://arxiv.org/abs/2507.15342 https://arxiv.org/pdf…

Eigenvalue distribution of some random matrices
In this paper, we investigate the eigenvalue distribution of a class of kernel random matrices whose $(i,j)$-th entry is $f(X_i,X_j)$ where $f$ is a symmetric function belonging to the Paley-Wiener space $\mathcal{B}_c$ and $(X_i)_{1\leq i \leq N}$ are i.i.d. random variables. We rigorously prove that, with high probability, the eigenvalues of these random matrices are well approximated by those of an underlying estimator. A particularly notable case is when $f=sinc$ , which has been widely…

Bounded powers of edge ideals: symmetric exchange binomials
Takayuki Hibi, Seyed Amin Seyed Fakhari
https://arxiv.org/abs/2507.11815 https://

Bounded powers of edge ideals: symmetric exchange binomials
It has been conjectured that the toric ideal of the base ring of a discrete polymatroid is generated by symmetric exchange binomials. In the present paper, we give several classes of discrete polymatroids which yield toric ideals generated by symmetric exchange binomials. Especially, we are interested in the discrete polymatroids arising from bounded powers of edge ideals of finite graphs.

Spontaneous Rotation of a Symmetric Inclusion in Chiral Active Bath
Abhra Puitandy, Shradha Mishra
https://arxiv.org/abs/2507.12811 https://

Spontaneous Rotation of a Symmetric Inclusion in Chiral Active Bath
We study the dynamics of a circular passive inclusion, termed a torquer, in a bath of chiral active Brownian particles. Despite being geometrically symmetric and non-motile, the torquer exhibits persistent rotation due to spatially inhomogeneous torques arising from angularly biased collisions with active particles. This interaction-driven symmetry breaking does not rely on shape anisotropy or external forcing. Through simulations, we identify two distinct regimes of rotation: one dominated by …

Detecting $k$-nonstretchability via a class of informationally complete symmetric measurements
Yan Hong, Mengjia Zhang, Limin Gao, Huaqi Zhou, Limei Zhang
https://arxiv.org/abs/2508.12817

Detecting $k$-nonstretchability via a class of informationally complete symmetric measurements
Multipartite entanglement characterization is a core problem in quantum information theory, with several classification schemes available. Among these, the $k$-stretchability, recently introduced [Szalay, Quantum 3, 204 (2019)], can be used to describe multipartite entanglement structure. Recently, a class of symmetric measurements (informationally complete $(s,t)$-POVMs) has been proposed [Siudzi$\textrm{ń}$ska, Phys. Rev. A \textbf{105}, 042209 (2022)] , which includes GSIC-POVMs and MUMs. I…

Skew-symmetric super-biderivations of the Hamiltonian superalgebra H(m, n; t)
Da Xu, Xiaoning Xu
https://arxiv.org/abs/2508.12067 https://arxiv.org/pdf/250…

Skew-symmetric super-biderivations of the Hamiltonian superalgebra H(m, n; t)
This paper aims to study the skew-symmetric super-biderivations of the Hamiltonian superalgebra H(m, n; t). Let H denote the Hamiltonian Lie superalgebra H(m, n; t) over a field of characteristic p > 2. Utilizing the abelian subalgebra TH and the weight space decomposition of H with respect to TH , we show the action of a skew-symmetric super-biderivation on the elements of TH and some specific elements of H. Moreover, we prove that all skew-symmetric super-biderivations of H are inner.

The CP2K Program Package Made Simple
Marcella Iannuzzi, Jan Wilhelm, Frederick Stein, Augustin Bussy, Hossam Elgabarty, Dorothea Golze, Anna Hehn, Maximilian Graml, Stepan Marek, Beliz Sertcan G\"okmen, Christoph Schran, Harald Forbert, Rustam Z. Khaliullin, Anton Kozhevnikov, Mathieu Taillefumier, Rocco Meli, Vladimir Rybkin, Martin Brehm, Robert Schade, Ole Sch\"utt, Johann V. Pototschnig, Hossein Mirhosseini, Andreas Kn\"upfer, Dominik Marx, Matthias Krack, J\"ur…

The CP2K Program Package Made Simple
CP2K is a versatile open-source software package for simulations across a wide range of atomistic systems, from isolated molecules in the gas phase to low-dimensional functional materials and interfaces, as well as highly symmetric crystalline solids, disordered amorphous glasses, and weakly interacting soft-matter systems in the liquid state and in solution. This review highlights CP2K's capabilities for computing both static and dynamical properties using quantum-mechanical and classical simu…

Symmetric power of higher dimensional varieties
Ashima Bansal, Supravat Sarkar, Shivam Vats
https://arxiv.org/abs/2508.12654 https://arxiv.org/pdf/2508.126…

Symmetric power of higher dimensional varieties
We study several properties of the symmetric power $S^mX$ of a smooth variety $X$. We describe the Picard and divisor class groups of $S^mX$ when $X$ is projective. We give a complete description of the stratification of $S^mX$ by iterated singular locus in terms of some combinatorial data regarding partitions of the integer $m.$ This gives a new viewpoint of a natural stratification of $S^mX$ by multiplicities.

Constructions of symmetric separable equivalences and their applications
Juxiang Sun, Guoqiang Zhao
https://arxiv.org/abs/2508.14401 https://arxiv.org/pdf/…

Constructions of symmetric separable equivalences and their applications
Let $Λ$ and $Γ$ be symmetrically separably equivalent Artin algebras. We prove that there exist symmetrical separable equivalences between certain endomorphism algebras of modules. As applications, we provide several methods to construct symmetrical separable equivalences from given ones and discuss when the rigidity dimension is an invariant under symmetrical separable equivalences. Moreover, we show that a symmetrical separable equivalence preserves the Frobenius-finite type, Auslander-type…

A Geometric View on Crossing-Symmetric Dispersion Relations
Joan Elias Miro, Andrea Guerrieri, Mehmet Asim Gumus, Ahmadullah Zahed
https://arxiv.org/abs/2509.14170 https://

A Geometric View on Crossing-Symmetric Dispersion Relations
We introduce a general framework for constructing dispersion relations using crossing-symmetric variables, leading to infinitely many distinct representations of the 2-to-2 scattering amplitude of identical scalars. Classical formulations such as the Auberson-Khuri crossing-symmetric dispersion relations (CSDRs), the Mahoux-Roy-Wanders relations, and the local CSDR, as well as fixed-t dispersion relations emerge as special cases. Within this setting we re-derive the null constraints from a geom…

The vanishing viscosity process for an eikonal equation in the radially symmetric setting
Fanchen Meng
https://arxiv.org/abs/2508.13230 https://arxiv.org/p…

The vanishing viscosity process for an eikonal equation in the radially symmetric setting
We study the vanishing viscosity method for the eikonal equation $|Du|=V$ in $B(0,1)$ with homogeneous Dirichlet boundary value condition. By assuming $V$ is radially symmetric and restricting attention to radially symmetric solutions, we construct explicit formulas for both the viscous solution $u^ε$ and the limiting solution $u$. We prove $u^ε\rightarrow u$ as $ε\rightarrow 0^+$ qualitatively and quantitatively derive an $ε|\log ε|$ type local convergence rate. Finall…

Some short notes on oriented line graphs and related matrices
Cyriac Antony, Jacob Antony
https://arxiv.org/abs/2507.13821 https://ar…

Some short notes on oriented line graphs and related matrices
The notion of oriented line graphs is introduced by Kotani and Sunada, and they are closely related to Hashimato's non-backtracking matrix. It is known that for regular graphs $G$, the eigenvalues of the adjacency matrix of the oriented line graph $\vec{L}(G)$ of $G$ are the reciprocals of the poles of the Ihara zeta function of $G$. We determine the characteristic polynomial of the adjacency matrix of the underlying undirected graph of $\vec{L}(G)$ and the skew-symmetric adjacency matrix of $\…

QKD Oracles for Authenticated Key Exchange
Kathrin H\"ovelmanns, Daan Planken, Christian Schaffner, Sebastian R. Verschoor
https://arxiv.org/abs/2509.12478 https://

QKD Oracles for Authenticated Key Exchange
Authenticated Key Exchange (AKE) establishes shared ('symmetric') cryptographic keys which are essential for secure online communication. AKE protocols can be constructed from public-key cryptography like Key Encapsulation Mechanisms (KEMs). Another approach is to use Quantum Key Distribution (QKD) to establish a symmetric key, which uses quantum communication. Combining post-quantum AKE and QKD appropriately may provide security against quantum attacks even if only one of the two approaches tu…

Spherically symmetric counterflow turbulence in open geometry
Tom\'a\v{s} Dunca, Filip Novotn\'y, Marek Tal\'i\v{r}, Bal\'azs Szalai, Nikita Ustinov, Ladislav Skrbek, Emil Varga
https://arxiv.org/abs/2509.14103

Spherically symmetric counterflow turbulence in open geometry
We report preliminary results on spherical thermal counterflow generated by a small central heater in an open geometry, an open bath of superfluid He~II, as closed-cell experiments could have introduced artifacts such as overheating and boundary-induced flows. In order to eliminate them, we measure second sound attenuation in a plane-parallel resonator. Our results are at variance with the previous experiments in closed spherical cavity that showed plateau in the steady-state vortex line densit…

Multidimensional gravity, black holes and mirror (topological) stars
Kirill A. Bronnikov, Sergei V. Bolokhov, Milena V. Skvortsova
https://arxiv.org/abs/2507.14603

Multidimensional gravity, black holes and mirror (topological) stars
We discuss static, spherically symmetric solutions to the 5D Einstein-Maxwell equations (belonging to wide classes of multidimensional solutions known at least from the 1990s) and select among them those which must observationally look like local objects whose surface reflects back particles or signals getting there, the so-called mirror stars (also called ``topological stars'' by some authors). Their significant parameters are the Schwarzschild mass $m$ and the magnetic charge $q$, such that $…

Poincar\'{e} Polynomials and Curvature Operators of Symmetric Spaces
Peter Petersen, James Stanfield
https://arxiv.org/abs/2508.11236 https://arxiv.org…

Poincaré Polynomials and Curvature Operators of Symmetric Spaces
We compute explicit formulas for the curvature operators and Poincaré polynomials of all compact irreducible symmetric spaces. We can easily derive the Poincaré polynomials using quantum numbers, giving a formula that mirrors the known formula for the Euler characteristic. For the curvature operators, we show that their maximum eigenvalue is always bounded above by the Einstein constant, with equality attained precisely by the Hermitian symmetric spaces.

The Small Phase Condition is Necessary for Symmetric Systems
Xiaokan Yang, Wei Chen, Li Qiu
https://arxiv.org/abs/2507.06617 https://…

The Small Phase Condition is Necessary for Symmetric Systems
In this paper, we show that the small phase condition is both sufficient and necessary to ensure the feedback stability when the interconnected systems are symmetric. Such symmetric systems arise in diverse applications. The key lies in that, for a complex symmetric and semi-sectorial matrix, the transformation matrix in its generalized sectorial decomposition can be taken to be real. Such a result fills the gap of phase based necessary condition for the feedback stability of symmetric systems,…

The Role of Rank in Mismatched Low-Rank Symmetric Matrix Estimation
Panpan Niu, Yuhao Liu, Teng Fu, Jie Fan, Chaowen Deng, Zhongyi Huang
https://arxiv.org/abs/2507.12019

The Role of Rank in Mismatched Low-Rank Symmetric Matrix Estimation
We investigate the performance of a Bayesian statistician tasked with recovering a rank-\(k\) signal matrix \(\bS \bS^{\top} \in \mathbb{R}^{n \times n}\), corrupted by element-wise additive Gaussian noise. This problem lies at the core of numerous applications in machine learning, signal processing, and statistics. We derive an analytic expression for the asymptotic mean-square error (MSE) of the Bayesian estimator under mismatches in the assumed signal rank, signal power, and signal-to-noise …

Spectral BBGKY: a scalable scheme for nonlinear Boltzmann and correlation kinetics
Shuai Lu, Shuzhe Shi
https://arxiv.org/abs/2507.14243 https://

Spectral BBGKY: a scalable scheme for nonlinear Boltzmann and correlation kinetics
The Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy provides a time-reversal-symmetric framework for describing the nonequilibrium evolution of many-body systems. Despite the success of Boltzmann-based numerical approaches, systematically extending beyond this lowest-order truncation to the full nonlinear BBGKY hierarchy remains a major challenge. Moreover, even at the Boltzmann level, accurately treating the nonlinear collision term still presents significant difficulties. Here we propos…

Robustness of Solutions of the Quantum Kinetic Equations in the Presence of Matter Density Fluctuations
Shashank Shalgar, Mariam Gogilashvili
https://arxiv.org/abs/2508.15747 ht…

Robustness of Solutions of the Quantum Kinetic Equations in the Presence of Matter Density Fluctuations
We investigate the role of fluctuations in the matter density on neutrino flavor evolution by studying their effects on the collision terms in the spherically symmetric quantum kinetics equations (QKEs). We solve the QKEs with varying radial resolution ($r_{\mathrm{bins}} = 150 \, , 1500 \, , 15000$) to assess numerical convergence in angular distributions, number densities, and energy spectra for four neutrino flavors ($ν_e$, $\barν_e$, $ν_x$, $\barν_x$). Our results demonstrate that the s…

Replaced article(s) found for quant-ph. https://arxiv.org/list/quant-ph/new
[1/2]:
- Exact solution of a non-Hermitian $\mathscr{PT}$-symmetric Heisenberg spin chain
Pradip Kattel, Parameshwar R. Pasnoori, Natan Andrei

Infinitely many non-radial solutions to a critical Choquard equation
Sabrina Caputo, Giusi Vaira
https://arxiv.org/abs/2507.15747 https://

Infinitely many non-radial solutions to a critical Choquard equation
In this paper we study a class of critical Choquard equations with a symmetric potential, i.e. we consider the equation $$-Δu +V(|x|) u =\left(|x|^{-μ}* |u|^{2^\star_μ}\right)|u|^{2^\star_μ-2}u,\quad\mbox{in}\quad\mathbb R^N$$ where $V(|x|)$ is a bounded, nonnegative and symmetric potential in $\mathbb R^N$ with $N\geq 5$, $0<μ\leq 4$, $*$ stands for the standard convolution and $2^\star_μ:=\frac{2N-μ}{N-2}$ is the upper critical exponent…

On the Multiary Algebraic Formulation of an Idempotent Symmetric Limit Convex Structure
Walter Briec
https://arxiv.org/abs/2509.14843 https://arxiv.org/pdf…

On the Multiary Algebraic Formulation of an Idempotent Symmetric Limit Convex Structure
In [14], B-convexity was defined as an appropriate Painlevé-Kuratowski limit of linear convexities. More recently, an alternative algebraic formulation over the entire Euclidean vector space was proposed in [9] and [10]. The issue with the definition presented in [14] is that it was not developed from an algebraic perspective, but rather as the upper limit of a sequence of generalized convex polytopes whose form was not explicitly given. In this paper, we build on recent work and provide an al…

Worldline Formulations of Covariant Fracton Theories
Filippo Fecit, Davide Rovere
https://arxiv.org/abs/2508.14591 https://arxiv.org/pdf/2508.14591

Worldline Formulations of Covariant Fracton Theories
We develop worldline formulations of covariant fracton gauge theories. These are a one-parameter family of gauge theories of a rank-two symmetric tensor field, invariant under a scalar gauge transformation involving a double derivative. These theories, which can be interpreted as linearized gravity theories invariant under longitudinal diffeomorphisms, provide a covariant framework for studying Lorentz-breaking fracton quasiparticles, which are excitations with restricted mobility due to dipole…

Skew-symmetric super-biderivations of the special odd Hamiltonian superalgebra SHO(n, n; t)
Da Xu, Xiaoning Xu
https://arxiv.org/abs/2508.12069 https://arx…

Skew-symmetric super-biderivations of the special odd Hamiltonian superalgebra SHO(n, n; t)
This paper aims to study the skew-symmetric super-biderivations of the special odd Hamiltonian superalgebra SHO(n, n; t). Let HO denote the odd Hamiltonian Lie superalgebra HO(n, n; t) and SHO the special odd Hamiltonian Lie superalgebra SHO(n, n; t) over a field of characteristic p > 2.Utilizing the abelian subalgebra TSHO and the weight space decomposition of HO with respect to TSHO , we show the action of a skew-symmetric super-biderivation on the elements of TSHO and some specific elements …

Quasimodular forms arising from Jacobi's theta function and special symmetric polynomials
Tewodros Amdeberhan, Leonid G. Fel, Ken Ono
https://arxiv.org/abs/2507.12352

Quasimodular forms arising from Jacobi's theta function and special symmetric polynomials
Ramanujan derived a sequence of even weight $2n$ quasimodular forms $U_{2n}(q)$ from derivatives of Jacobi's weight $3/2$ theta function. Using the generating function for this sequence, one can construct sequences of quasimodular forms of all nonnegative integer weights with minimal input: a weight 1 modular form and a power series $F(X)$. Using the weight 1 form $θ(q)^2$ and $F(X)=e^{X/2}$, we obtain a sequence $\{Y_n(q)\}$ of weight $n$ quasimodular forms on $Γ_0(4)$ whose symmetric functi…

Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The $\lambda_N$-Jellium model
F\'elix Desrochers, Joe Huxford, Mark R. Hirsbrunner, Yong Baek Kim
https://arxiv.org/abs/2509.15300

Electronic Crystal Phases in the Presence of Non-Uniform Berry Curvature and Tunable Berry Flux: The $λ_N$-Jellium model
Recent experiments on multilayer graphene systems have rekindled interest in electronic crystal phases in two dimensions -- but now for phases enriched by non-trivial quantum geometry. In this work, we introduce a simple continuum model with tunable Berry curvature distribution and total flux, enabling systematic study of crystallization in geometrically nontrivial bands. In the noninteracting limit, the addition of a C6-symmetric periodic potential yields a rich phase diagram, for which we pro…

Exploring the dynamics of coincident f(Q) gravity in the presence of DBI-essence scalar field
Ratul Mandal, Ujjal Debnath, Anirudh Pradhan
https://arxiv.org/abs/2507.13406

Exploring the dynamics of coincident f(Q) gravity in the presence of DBI-essence scalar field
In theoretical cosmology, symmetric teleparallel gravity or $f(Q)$ gravity based on nonmetricity tensor Q has become an interesting alternative to General relativity in recent years. The present research paper contains a rigorous dynamical system analysis of coincident f (Q) gravity in the presence of a generalized DBI essence scalar field. We have considered two different models of coincident f(Q) gravity, such as power law model $f(Q) = Q + nQ^m$ and exponential model $f(Q) = Q e^{\frac{βQ_0…

Harmonic functions for recurrent symmetric $\alpha$-stable processeses with non-local perturbations
Kaneharu Tsuchida
https://arxiv.org/abs/2509.13918 https://

Harmonic functions for recurrent symmetric $α$-stable processeses with non-local perturbations
Let ${\mathbf M}$ be the recurrent symmetric (relativistic) $α$-stable process on ${\mathbb R}^d$. Let ${\mathcal H}^{μ+ F} (:= {\mathcal H} + μ+ F)$ be a Schrödinger type operator with local and non-local perturbations $μ$ and $F$. If $μ$ and $F$ satisfy suitable conditions associated with Kato class, we prove the existence of ground state for a Schrödinger type operator relating to ${\mathcal H}^{μ+ F}$. Furthermore, we prove the ground state becomes a probabilistically harmonic funct…

Helicity amplitudes of $N(1520)$ and $N(1535)$ including pentaquark components
Kai Xu, Attaphon Kaewsnod, Zheng Zhao, Ayut Limphirat, Yupeng Yan
https://arxiv.org/abs/2508.15000

Helicity amplitudes of $N(1520)$ and $N(1535)$ including pentaquark components
We investigate the helicity amplitudes of the $N(1520)$ and $N(1535)$ resonances in the electromagnetic transition process $γ^*p\to N^*$, where the $N(1520)$ and $N(1535)$ are assumed to include both the $L=1$ three-quark and $L=0$ spatial symmetric $q^4\bar q$ pentaquark components. The helicity transition amplitudes $A_{1/2}$, $A_{3/2}$ (for spin 3/2 states) and $S_{1/2}$ are computed within the constituent quark model. The inclusion of the $q^4 \bar q$ pentaquark components via the $γ^*\to…

Local limit theorems on relatively hyperbolic groups with respect to virtually nilpotent subgroups
Matthieu Dussaule
https://arxiv.org/abs/2507.15408 https…

Local limit theorems on relatively hyperbolic groups with respect to virtually nilpotent subgroups
Given a probability measure on a finitely generated group, the local limit problem consists in finding asymptotics of $p_n(e,e)$, the probability that the random walk at time $n$ is at the origin. We give the classification of all possible local limit theorems, up to bounded error, for finitely supported, symmetric, admissible probability measures on a relatively hyperbolic group with respect to virtually nilpotent subgroups.

From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
Kiran Babasaheb Estake, T. R. Vishnu, Dibyendu Roy
https://arxiv.org/abs/2508.14560

From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
We propose a Hermitian quadratic bosonic model (QBH) whose dynamical matrix exhibits distinct topological and dynamical phenomena depending on whether the hopping and pairing amplitudes are real or purely imaginary. In the real-parameter regime, the dynamical matrix is unitarily equivalent to four decoupled copies of the sublattice-symmetric non-Hermitian Su-Schrieffer-Heeger (nSSH2) model, thereby inheriting its topological phases and energy spectrum-including the Möbius phase, a gapless topo…

Non-negative curvature on certain product manifolds
Wen Shen
https://arxiv.org/abs/2508.15194 https://arxiv.org/pdf/2508.15194

Non-negative curvature on certain product manifolds
Let $G/H$ be a closed, simply connected homogeneous manifold. Suppose every stable class of real vector bundles over $G/H$ contains a homogeneous bundle. Then, for any closed, simply connected smooth manifold $M$ homotopy equivalent to $G/H$, there exists $n>\mathrm{dim}(M)$ such that the product manifold $M\times S^{n}$ admits a metric with non-negative sectional curvature. Many homogeneous manifolds satisfy this assumption, including simply connected compact rank-one symmetric spaces, and amo…

On Hilbert series of Koszul operads and a classification result for set-operads
Paul Laubie
https://arxiv.org/abs/2509.14419 https://arxiv.org/pdf/2509.144…

On Hilbert series of Koszul operads and a classification result for set-operads
Motivated by numerous examples in the literature, we state a conjecture on the Hilbert series of Koszul symmetric operads generated by one element of arity $2$. We prove this conjecture for all Koszul symmetric set-operads generated by one element of arity $2$ by explicitly classifying those. There are $11$ such operads; $4$ of them are new.

Electron-neutrino lepton number crossings: variations with the supernova core physics
Marie Cornelius (Niels Bohr Institute), Irene Tamborra (Niels Bohr Institute), Malte Heinlein (MPI Astrophysics, TUM), Shashank Shalgar (Niels Bohr Institute), Hans-Thomas Janka (MPI Astrophysics)
https://arxiv.org/abs/2507.13429

Electron-neutrino lepton number crossings: variations with the supernova core physics
A crucial ingredient affecting fast neutrino flavor conversion in core-collapse supernovae (SNe) is the shape of the angular distribution of the electron-neutrino lepton number (ELN). The presence of an ELN crossing signals favorable conditions for flavor conversion. However, the dependence of ELN crossings on the SN properties is only partially understood. We investigate a suite of 12 spherically symmetric neutrino-hydrodynamics simulations of the core collapse of a SN with a mass of $18.6 M_\…

Black Hole Mass/Charge Relation and Weak No-hair Theorem Conjecture
Guan-Yi Lu, Meng-Nan Yang, H. Lu
https://arxiv.org/abs/2508.14158 https://arxiv.org/pdf…

Black Hole Mass/Charge Relation and Weak No-hair Theorem Conjecture
We consider Einstein gravity minimally coupled to two Maxwell fields and one dilaton scalar. We study the electrically-charged spherically-symmetric and static solutions that are asymptotic to Minkowski spacetime. General solutions are described by four independent parameters: mass $M$, two electric charges $(Q_1,Q_2)$ and the scalar charge $Σ$. For black holes, the scalar charge is not independent, but a function of $(M,Q_1,Q_2)$. We provide a set of formulae relating the mass to the charges,…

Equivariant Free Resolutions of Sequences of Symmetric Module
Michael Morrow, Uwe Nagel
https://arxiv.org/abs/2507.11650 https://arxi…

Equivariant Free Resolutions of Sequences of Symmetric Module
Given a sequence of related modules $M_n$ over a sequence of related Noetherian polynomial rings, where each $M_n$ is a representation of the symmetric group on $n$ letters, one may ask how to simultaneously compute an equivariant free resolution of each $M_n$. In this article, we address this question. Working in the setting of FI-modules over a Noetherian polynomial FI-algebra, we provide an algorithm for computing syzygies and FI-equivariant differentials. As an application, we show how this…

On Naturally and Weakly Mal'tsev Categories
Nelson Martins-Ferreira
https://arxiv.org/abs/2508.13315 https://arxiv.org/pdf/2508.13315

On Naturally and Weakly Mal'tsev Categories
We explore a hierarchy of notions in categorical algebra: Mal'tsev categories (where every reflexive relation is symmetric); naturally Mal'tsev categories (where every reflexive graph underlies a unique internal groupoid structure, also known as the Lawvere Condition); and weakly Mal'tsev categories (defined via the joint epimorphicity of local product injections). While varying in generality and historical prominence, these notions can be uniformly described using suitable classes of spans and…

Replaced article(s) found for gr-qc. https://arxiv.org/list/gr-qc/new
[1/1]:
- Locally Rotationally Symmetric spacetimes of type II in $f(\mathcal{Q})$ gravity
Fabrizio Esposito, Sante Carloni, Stefano Vignolo

On the structure and skeletals of principal ideal graphs of inverse semigroups
C S Preenu, R S Indu, Sijo George
https://arxiv.org/abs/2509.15656 https://a…

On the structure and skeletals of principal ideal graphs of inverse semigroups
The principal left ideal graph of a semigroup is a simple graph whose vertices are the non-zero elements of the semigroup, and two vertices are adjacent if their principal left ideals intersect non-trivially. In this paper, we study the structure of the principal ideal graphs of inverse semigroups, particularly symmetric inverse semigroups. We also introduce the concept of skeletal of a graph and show that the principal ideal graph of an inverse semigroup has a skeletal, which is a simple graph…

Symmetrizing relativistic three-body partial wave amplitudes
Andrew W. Jackura, Nicholas C. Chambers, Ra\'ul A. Brice\~no
https://arxiv.org/abs/2507.14098

Symmetrizing relativistic three-body partial wave amplitudes
S matrix principles and symmetries impose constraints on three-particle scattering amplitudes, which can be formulated as a class of integral equations for their partial wave projections. However, these amplitudes are typically expressed in an asymmetric basis, where one of the initial and final state particles is singled out, and all quantum numbers are defined relative to this spectator. In this work, we show how to construct symmetric partial wave amplitudes, which have been symmetrized over…

Euclidean Wormholes and Gravitational States
Alexandre Belin
https://arxiv.org/abs/2508.14165 https://arxiv.org/pdf/2508.14165

Euclidean Wormholes and Gravitational States
Euclidean wormholes are known to encode important non-perturbative effects in the physics of quantum black holes. In this paper, we discuss the slicing of Euclidean wormholes along a time-reflection symmetric slice which treats half of the Euclidean geometry as a gravitational machinery to produce a semi-classical state. This type of state preparation is different from Hartle-Hawking states prepared with the CFT path integral, such as the thermofield-double state. Nevertheless, the two differen…

Borel--Serre type bordifications and Canonical Pairs for Loop groups
Manish M. Patnaik, Punya Plaban Satpathy
https://arxiv.org/abs/2507.13980 https://

Borel--Serre type bordifications and Canonical Pairs for Loop groups
To the symmetric space of the (positive half) of a real loop group, we attach a Borel--Serre type bordification and equip it with a Hausdorff topology. The attached boundary, indexed by certain rational parabolics of the loop group, is shown to be homotopic to an affine, rational Tits building. A loop analogue of an arithmetic group is also shown to act continuously on the bordification and its quotient by this action is studied using the reduction theory of H. Garland. While the quotient is no…

Symmetric quasisymmetric Schur-like functions
Maria Esipova, Jinting Liang, Stephanie van Willigenburg
https://arxiv.org/abs/2507.08083 https://

Symmetric quasisymmetric Schur-like functions
In this paper we classify when (row-strict) dual immaculate functions and (row-strict) extended Schur functions, as well as their skew generalizations, are symmetric. We also classify when their natural variants, termed advanced functions, are symmetric. In every case our classification recovers classical skew Schur functions.

Pathwise regularity of solutions for a class of elliptic SPDEs with symmetric L\'evy noise
Juan J. Jim\'enez
https://arxiv.org/abs/2507.12656 https…

Pathwise regularity of solutions for a class of elliptic SPDEs with symmetric Lévy noise
In this article, we investigate the existence and uniqueness of random-field solutions to the elliptic SPDE $-\mathcal{L}u=\dotξ$ on a bounded domain $D$ with Dirichlet boundary conditions $u=0$ on $\partial D$, driven by symmetric Lévy noise $\dotξ$. Under general sufficient conditions on the coefficients of the second-order operator $\mathcal{L}$, we prove the existence of a mild solution via the corresponding Green's function and show that the same framework applies to the spectral fracti…

Chameleon Gravity as an Alternative to Dark Matter
Raziyeh Zaregonbadi, Nasim Saba, Mehrdad Farhoudi
https://arxiv.org/abs/2507.13972 https://

Chameleon Gravity as an Alternative to Dark Matter
By studying the chameleon gravity on galaxy scales, we investigate the effects of the chameleon dark matter. To perform this task, we consider the dynamics of the chameleon scalar field in the region of galactic halos in static spherically symmetric spacetimes that differ only slightly from classical general relativity, but have similar symmetry behind this region. Hence, we demonstrate its ability to act as dark matter. In fact, by obtaining the expression for the tangential speed in this regi…

Exact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real forms
Eric D'Hoker, Michael Gutperle, Christoph F. Uhlemann
https://arxiv.org/abs/2508.14959

Exact solutions to complex Type IIB supergravity for complex superalgebra $F(4)$ and its real forms
We construct the general local solutions to complexified Type IIB supergravity which are invariant under the complexified Lie superalgebra $F(4)$. The geometry is a product of complexified maximally symmetric spaces $\mathcal M_{6 {\mathbb C}}$ and $\mathcal M_{2 {\mathbb C}}$ warped over a complexified surface $Σ_{\mathbb C}$. We classify the reality conditions that may be imposed consistently to obtain real form solutions within real forms of complex Type IIB supergravity. The latter compris…

Existence, asymptotic behaviors, and high-dimensional uniqueness of topological solutions to the skew-symmetric Chern-Simons system on lattice graphs
Honggang Liu
https://arxiv.org/abs/2509.14538

Existence, asymptotic behaviors, and high-dimensional uniqueness of topological solutions to the skew-symmetric Chern-Simons system on lattice graphs
In this paper, we consider the topological solutions to the skew-symmetric Chern-Simons system on lattice graphs: $$\left\{\begin{aligned} Δu &=λ\mathrm{e}^{\upsilon}(\mathrm{e}^{u}-1)+4π\sum\limits_{j=1}^{k_1}m_jδ_{p_j}, Δ\upsilon&=λ\mathrm{e}^{u}(\mathrm{e}^{\upsilon}-1)+4π\sum\limits_{j=1}^{k_2}n_jδ_{q_j}, \end{aligned} \right. $$ here, $λ\in\mathbb{R}_+$, $k_1$ and $k_2$ are two positive integers, $m_j\in\mathbb{N}\, (j=1,2,\cdot\cdot\cdot,k_1)$, $n_j\in\mathbb{N}\,(j=1,2,\cdot\cdo…

Waldschmidt constants of symmetric sets of points in $\mathbb{P}^3$
Sebastian Calvo, Jack Huizenga, Tomasz Szemberg
https://arxiv.org/abs/2507.11888 https:…

Waldschmidt constants of symmetric sets of points in $\mathbb{P}^3$
Configurations of points defined by complex reflection groups have attracted a lot of attention recently in several directions of research, e.g., the containment problem between ordinary and symbolic powers of ideals, in the theory of unexpected hypersurfaces, in the study of sets of points whose general projections are complete intersections and in the ideas revolving around the Bounded Negativity Conjecture. In order to understand these configurations better several attempts have been underta…

Antiferromagnetism and Stripe Channel Order in the $\mathrm{SU}(N)$-Symmetric Two-Channel Kondo Lattice Model
Elyasaf Y. Cohen, Fakher F. Assaad, Snir Gazit
https://arxiv.org/abs/2509.12311

Antiferromagnetism and Stripe Channel Order in the $\mathrm{SU}(N)$-Symmetric Two-Channel Kondo Lattice Model
We carry out large-scale, sign-problem-free determinant quantum Monte Carlo simulations of the square lattice $\mathrm{SU}(N)$-symmetric two-channel Kondo lattice model at half-filling. We map out the zero-temperature phase diagram for $N = 2, 4, 6$, and $8$, as a function of the Kondo coupling strength. In the weak-coupling regime, we observe antiferromagnetic order of the localized moments. Remarkably, for $N \geq 6$, sufficiently strong Kondo coupling induces spontaneous channel symmetry bre…

Polars and antipodal sets of generalized $s$-manifolds
Shinji Ohno, Takashi Sakai
https://arxiv.org/abs/2508.11855 https://arxiv.org/pdf/2508.11855

Polars and antipodal sets of generalized $s$-manifolds
In this paper, we introduce the notion of generalized $s$-manifolds, which is a generalization of symmetric spaces. Then we give a method to construct generalized $s$-manifolds and present some typical examples. We study polars and antipodal sets of generalized $s$-manifolds aiming to extend the results on compact symmetric spaces due to Chen and Nagano.

The Blockwise Navarro Alperin Weight Conjecture for Double Covers of Symmetric and Alternating Groups
Yucong Du, Xin Huang, Jiping Zhang
https://arxiv.org/abs/2509.13673 https:/…

The Blockwise Navarro Alperin Weight Conjecture for Double Covers of Symmetric and Alternating Groups
We prove the blockwise Navarro Alperin weight conjecture for double covers of symmetric and alternating groups.

Symmetric tensor portals to dark matter I: creation of dark scalars
Brian Dignean, Alexander J. Magnus, Rainer Dick
https://arxiv.org/abs/2509.11010 https://

Symmetric tensor portals to dark matter I: creation of dark scalars
We examine the creation of scalar dark matter through a symmetric tensor portal. We find that both freeze-in and thermal freeze-out through a symmetric tensor mediator can create scalar dark matter. The required tensor masses for freeze-in are much larger than for freeze-out for the same dark-matter mass, in agreement with the nonthermalization assumption in freeze-in scenarios.

Generalized Symmetries and Deformations of Symmetric Product Orbifolds
Nathan Benjamin, Suzanne Bintanja, Yu-Jui Chen, Michael Gutperle, Conghuan Luo, Dikshant Rathore
https://arxiv.org/abs/2509.12180 …

Generalized Symmetries and Deformations of Symmetric Product Orbifolds
We construct generalized symmetries in two-dimensional symmetric product orbifold CFTs $\text{Sym}^N(\mathcal{T}),$ for a generic seed CFT $\mathcal{T}$. These symmetries are more general than the universal and maximally symmetric ones previously constructed. We show that, up to one fine-tuned example when the number of copies $N$ equals four, the only symmetries that can be preserved under twisted sector marginal deformations are invertible and maximally symmetric. The results are obtained in …

Area-charge inequalities and rigidity of time-symmetric initial data sets
Tiarlos Cruz, Abra\~ao Mendes
https://arxiv.org/abs/2507.13040 https://

Area-charge inequalities and rigidity of time-symmetric initial data sets
In this paper, we establish new area-charge inequalities for the boundary of time-symmetric Einstein-Maxwell initial data sets, in both compact and noncompact cases, under the dominant energy condition. These inequalities lead to novel rigidity theorems with no analogues in the uncharged setting. In the noncompact case, our result is obtained by applying Gromov's $μ$-bubble technique in a new geometric context.

RSK and Quantum Symmetric Functions: A Combinatorial Approach
Eddy Pariguan, Jhoan Sierra V
https://arxiv.org/abs/2509.07912 https://arxiv.org/pdf/2509.079…

RSK and Quantum Symmetric Functions: A Combinatorial Approach
We explore an application of the Robinson-Schensted-Knuth (RSK) algorithm in the context of the quantum product of multi-symmetric functions. After reviewing the combinatorial foundations of quantum symmetric functions, we establish connections with transportation polytopes. Our approach highlights the combinatorial richness underlying the star product of symmetric functions.

Emergence of Symmetry in a System of Distinguishable but Identical Particles
Allan Tameshtit
https://arxiv.org/abs/2509.11779 https://arxiv.org/pdf/2509.11…

Emergence of Symmetry in a System of Distinguishable but Identical Particles
Instead of the conventional construction of symmetric and antisymmetric states by abruptly projecting with the symmetrizer or antisymmetrizer, this paper investigates rapid but continuous symmetrization via environment-induced decoherence. Density operators are transformed to a symmetric observable via a semigroup map obtained from an interacting Hamiltonian. Likewise, a completely positive dynamical map transforms a completely asymmetric state to either a symmetric or antisymmetric state. The …

Quantum-Corrected Thermodynamics and Plasma Lensing in Non-Minimally Coupled Symmetric Teleparallel Black Holes
Erdem Sucu, \.Izzet Sakall{\i}, \"Ozcan Sert, Yusuf Sucu
https://arxiv.org/abs/2508.11076

Quantum-Corrected Thermodynamics and Plasma Lensing in Non-Minimally Coupled Symmetric Teleparallel Black Holes
We investigate the thermodynamic and optical signatures of electrically charged black holes (BHs) in symmetric teleparallel gravity (STPG) with non-minimal electromagnetic coupling, incorporating quantum corrections and plasma dispersion effects. The BH solution, characterized by a coupling parameter $k$, generalizes the Reissner-Nordström spacetime through power-law modifications to electromagnetic terms in the metric function. We implement exponential corrections to the Bekenstein-Hawking en…

Spherically symmetric collapsing solution in the form of shadow wave
Marko Nedeljkov, Sanja Ru\v{z}i\v{c}i\'c
https://arxiv.org/abs/2508.12492 https://…

Spherically symmetric collapsing solution in the form of shadow wave
This paper deals with isothermal Euler-Poisson system which is used to model collapse of self-gravitating Newtonian star. Density dependent viscosity term is added on the right-hand side of momentum equation and it has been proved that there exists stable shadow wave solution with unbounded density at the origin. This results is extended to the vanishing pressure case.

From Symmetric Toeplitz Hamiltonians to Quantum Circuits
Rayan Trabelsi
https://arxiv.org/abs/2508.10167 https://arxiv.org/pdf/2508.10167

From Symmetric Toeplitz Hamiltonians to Quantum Circuits
This work introduces a quantum circuit synthesis framework for simulating the unitary time evolution under a subclass of symmetric Toeplitz Hamiltonians by decomposing them into specific diagonal matrices $M_k$. These matrices are then classified, to achieve significant simplification, into, $M_k$ when $k$ is a power of two, and congruence classes with constant coefficients. Finally, we construct the explicit quantum circuit for the one-dimensional discrete Poisson equation. This research was c…

Quantum Corner Polynomials: A Generalization of Super Macdonald Polynomials and Their VOA Correspondence
Panupong Cheewaphutthisakun, Jun'ichi Shiraishi, Keng Wiboonton
https://arxiv.org/abs/2508.12267

Quantum Corner Polynomials: A Generalization of Super Macdonald Polynomials and Their VOA Correspondence
In this paper, we introduce a family of partially symmetric polynomials, which we call quantum corner polynomials, as a generalization of the Sergeev-Veselov super Macdonald polynomials. We show that these quantum corner polynomials are precisely the partially symmetric polynomials corresponding to the quantum corner VOAs. Furthermore, we provide a detailed proof of the partial symmetricity of these polynomials.

Monotonicity properties of the Robin torsion function in a class of symmetric planar domains
Qinfeng Li, Juncheng Wei, Ruofei Yao
https://arxiv.org/abs/2509.14648 https://

Monotonicity properties of the Robin torsion function in a class of symmetric planar domains
We prove the monotonicity property of the Robin torsion function in a smooth planar domain $Ω$ with a line of symmetry, provided that the Robin coefficient $β$ is greater than or equal to the negative of the boundary curvature $κ$ (i.e., $β\geq -κ$ on $\partialΩ$). We also show that this condition is, in a certain sense, sharp by constructing a counterexample.

On approximate quantum error correction for symmetric noise
Gereon Ko{\ss}mann, Julius A. Zeiss, Omar Fawzi, Mario Berta
https://arxiv.org/abs/2507.12326 h…

On approximate quantum error correction for symmetric noise
We revisit the extendability-based semi-definite programming hierarchy introduced by Berta et al. [Mathematical Programming, 1 - 49 (2021)], which provides converging outer bounds on the optimal fidelity of approximate quantum error correction (AQEC). As our first contribution, we introduce a measurement-based rounding scheme that extracts inner sequences of certifiably good encoder-decoder pairs from this outer hierarchy. To address the computational complexity of evaluating fixed levels of th…

Phases of 2d Gauge Theories and Symmetric Mass Generation
Rishi Mouland, David Tong, Bernardo Zan
https://arxiv.org/abs/2509.12305 https://arxiv.org/pdf/25…

Phases of 2d Gauge Theories and Symmetric Mass Generation
We study the dynamics and phase structure of Abelian gauge theories in $d=1+1$ dimensions. These include $U(1)$ gauge theory coupled to a scalar and a fermion, as well as the two-flavour Schwinger model with different charges. Both theories exhibit a surprisingly rich phase diagram as masses are varied, with both $c=1$ and $c=1/2$ critical lines or points. We build up to the study of 2d chiral gauge theories, which hold particular interest because they provide a mechanism for symmetric mass gen…

Inflation in Myrzakulov $F(R,T)$ Gravity: A Comparative Study in Metric, Symmetric Teleparallel, and Weitzenb\"{o}ck Formalisms
Davood Momeni, Ratbay Myrzakulov
https://arxiv.org/abs/2507.11753

Inflation in Myrzakulov $F(R,T)$ Gravity: A Comparative Study in Metric, Symmetric Teleparallel, and Weitzenböck Formalisms
We present a unified treatment of cosmic inflation within the framework of Myrzakulov Gravity, exploring its realization in three different formalisms: metric (curvature-based), teleparallel (torsion-based), and symmetric teleparallel (non-metricity-based). For each case, we derive the corresponding field equations in a flat FLRW background, study inflationary solutions driven by a scalar field, and compute observable quantities such as the scalar spectral index \( n_s \) and the tensor-to-scal…

Pseudospectrum and time-domain analysis of the EFT corrected black holes
Li-Ming Cao, Ming-Fei Ji, Liang-Bi Wu, Yu-Sen Zhou
https://arxiv.org/abs/2508.13894 https://

Pseudospectrum and time-domain analysis of the EFT corrected black holes
We study the linear perturbations of a spherically symmetric black hole corrected by dimension-6 terms in EFT of gravity. The solution is asymptotically flat and characterized by two parameters -- a mass parameter $M$ and a dimensionless parameter $\varepsilon$ related to the EFT length scale $l$, and the perturbation equation incorporates a velocity factor which is not constant. The quasinormal modes (QNMs) and time-domain waveforms are studied within the hyperboloidal framework. This approach…

Replaced article(s) found for hep-th. https://arxiv.org/list/hep-th/new
[1/1]:
- On palindromic numerators of bigraded symmetric orbifold Hilbert series and Kostka-Foulkes polyno...
Yannick Mvondo-She

On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
Nishanth Gudapati
https://arxiv.org/abs/2507.08326 https://arxiv.org…

On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
The lack of a positive-definite and conserved energy is a serious obstacle in the black hole stability problem. In this work, we will show that there exists a positive-definite and conserved Hamiltonian energy for axially symmetric linear perturbations of the exterior of Kerr black hole spacetimes. In the first part, based on the Hamiltonian dimensional reduction of 3+1 axially symmetric, Ricci-flat Lorentzian spacetimes to a 2+1 Einstein-wave map system with the negatively curved hyperbolic 2-…

Compact stars in Einstein-scalar-Gauss-Bonnet gravity: regular and divergent scalar field configurations
Roberto D. Alba Q., Javier Chagoya, Armando A. Roque
https://arxiv.org/abs/2508.13273

Compact stars in Einstein-scalar-Gauss-Bonnet gravity: regular and divergent scalar field configurations
We investigate static, spherically symmetric solutions in Einstein-scalar-Gauss-Bonnet gravity non-minimally coupled to a massless real scalar field, both in vacuum and in the presence of fermionic matter. Focusing on a specific quadratic scalar-Gauss-Bonnet coupling, we identify two distinct classes of compact objects: one with a regular scalar field at the origin -- connected to general relativity in an appropriate limit -- and another {one} with a divergent scalar field at the origin but a r…

Echoes and quasinormal modes of asymmetric black bounces
Alana C. L. Santos, Leandro A. Lessa, Roberto V. Maluf, Gonzalo J. Olmo
https://arxiv.org/abs/2508.11096 https://…

Echoes and quasinormal modes of asymmetric black bounces
We study quasinormal modes and echoes of symmetric and asymmetric black bounce solutions generated by anisotropic fluids within the framework of general relativity. We derive the effective potential governing massless scalar fields and compute the corresponding quasinormal mode spectra using three independent methods: sixth-order WKB, Pöschl-Teller and time-domain evolution. Our results show that symmetric black bounce configurations with horizons yield a standard single-barrier potential, whi…

Listening to black mirrors with gravitational radiation
Pau Amaro Seoane
https://arxiv.org/abs/2508.13272 https://arxiv.org/pdf/2508.13272

Listening to black mirrors with gravitational radiation
The existence of curvature singularities and the information and firewall paradoxes are significant problems for the conventional black hole model. The black mirror hypothesis provides a CPT-symmetric alternative to the classical description of black hole, offering a novel solution to these long-standing issues. We show that classical black holes can, in principle, be distinguished from black mirrors observationally, by using gravitational waves. The principal challenge is to identify a unique,…