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Replaced article(s) found for math.RT. https://arxiv.org/list/math.RT/new/
[1/1]:
Starfish lemma via birational quasi-isomorphisms
https://…

Mirror Symmetry in Geometric Constraints: Analytic and Riemann-Roch Perspectives
Dongzhe Zheng
https://arxiv.org/abs/2506.06610 https://

Mirror Symmetry in Geometric Constraints: Analytic and Riemann-Roch Perspectives
Building upon the discovery of mirror symmetry phenomena in compatible pair Spencer complexes, this paper develops rigorous analytical foundations through systematic application of elliptic perturbation theory and characteristic class analysis. We establish a comprehensive multi-level framework revealing the mathematical mechanisms underlying the symbolic transformation $(D,λ) \mapsto (D,-λ)$: metric invariance analysis via Spencer metric theory, topological isomorphisms through elliptic oper…

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles
Dongzhe Zheng
https://arxiv.org/abs/2506.00728

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles
This paper develops a mirror symmetry theory of Spencer cohomology within the geometric framework of constrained systems on principal bundles, revealing deep symmetric structures in constraint geometry. Based on compatible pairs $(D,λ)$ under strong transversality conditions, we construct a systematic family of mirror transformations: from basic sign mirrors $λ\mapsto -λ$ to general automorphism-induced mirrors $λ\mapsto (dϕ)^*(λ)$. Our core result proves that these transformations preser…

Simplicial properadic homotopy
Eric Hoffbeck, Johan Leray, Bruno Vallette
https://arxiv.org/abs/2505.22004 https://arxiv.org/pdf/2505…

Simplicial properadic homotopy
In this paper, we settle the homotopy properties of the infinity-morphisms of homotopy (bial)-gebras over properads, i.e. algebraic structures made up of operations with several inputs and outputs. We start by providing the literature with characterizations for the various types of infinity-morphisms, the most seminal one being the equivalence between infinity-quasi-isomorphisms and zig-zags of quasi-isomorphisms which plays a key role in the study the formality property. We establish a simplic…

This https://arxiv.org/abs/2505.15672 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Explicit isomorphisms for the symmetry algebras of continuous and discrete isotropic oscillators
We present a detailed study of a parametric Lie algebra encompassing the symmetry algebras of the isotropic oscillator (for positive, purely imaginary and zero frequency) and one of its possible deformations. We show that such a Lie algebra appears naturally also within the context of maximally superintegrable discretizations of the isotropic harmonic oscillator. After an in-depth analysis of the properties characterizing the Lie algebra in the purely abstract setting, we construct explicit iso…

Dual realizations of Bergman spaces on strongly convex domains
Agniva Chatterjee
https://arxiv.org/abs/2506.02913 https://arxiv.org/p…

Dual realizations of Bergman spaces on strongly convex domains
The Fantappiè and Laplace transforms realize isomorphisms between analytic functionals supported on a convex compact set $K\subset{\mathbb C}^n$ and certain spaces of holomorphic functions associated with $K$. Viewing the Bergman space of a bounded domain in ${\mathbb C}^n$ as a subspace of the space of analytic functionals supported on its closure, the images of the restrictions of these transforms have been studied in the planar setting. For the Fantappiè transform, this was done for simply…

This https://arxiv.org/abs/2304.05500 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Rigidity for von Neumann algebras of graph product groups II. Superrigidity results
In \cite{CDD22} we investigated the structure of $\ast$-isomorphisms between von Neumann algebras $L(Γ)$ associated with graph product groups $Γ$ of flower-shaped graphs and property (T) wreath-like product vertex groups as in \cite{CIOS21}. In this follow-up we continue the structural study of these algebras by establishing that these graph product groups $Γ$ are entirely recognizable from the category of all von Neumann algebras arising from an arbitrary non-trivial graph product group wit…

On Generalised Danielewski Surfaces over fields of arbitrary characteristic
Debojyoti Saha
https://arxiv.org/abs/2506.01457 https://a…

On Generalised Danielewski Surfaces over fields of arbitrary characteristic
In this paper we study exponential maps ($\mathbb{G}_a$-actions) on the family of affine two dimensional surfaces of the form $f(x)y=ϕ(x,z)$ over arbitrary fields, describe the Makar-Limanov invariant and Derksen invariant of these surfaces, give a complete characterization of isomorphisms between such surfaces and display a subfamily which provides counterexamples to the cancellation problem.

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Liat Kessler, Nikolas Wardenski
https://arxiv.org/abs/2505.14000 https://

On isomorphisms of semi-free Hamiltonian $S^1$-manifolds and fixed point data
Following Gonzales, we answer the question of whether the isomorphism type of a semi-free Hamiltonian $S^1$-manifold of dimension six is determined by certain data on the critical levels. We first give counter examples showing that Gonzales' assumptions are not sufficient for a positive answer. Then we prove that it is enough to further assume that the reduced spaces of dimension four are symplectic rational surfaces and the interior fixed surfaces are restricted to at most one level. The addit…