Tootfinder

Positivity properties of canonical bases
Jiepeng Fang, Xuhua He
https://arxiv.org/abs/2510.12154 https://arxiv.org/pdf/2510.12154

Positivity properties of canonical bases
We prove that the canonical basis of a modified quantum group $\dot{\mathbf{U}}$ exhibits strong positivity properties for the canonical basis elements arising from spherical parabolic subalgebras. Our main result establishes that the structure constants for both the multiplication with arbitrary canonical basis elements in $\dot{\mathbf{U}}$ and the action on the canonical basis elements of arbitrary tensor products of simple lowest and highest weight modules by these elements belong to $\math…

Temperature and conditions for thermalization after canonical quenches
Lennart Dabelow
https://arxiv.org/abs/2510.12696 https://arxiv.org/pdf/2510.12696

Temperature and conditions for thermalization after canonical quenches
We consider quenches of a quantum system that is prepared in a canonical equilibrium state of one Hamiltonian and then evolves unitarily in time under a different Hamiltonian. Technically, our main result is a systematic expansion of the pre- and post-quench canonical ensembles in the quench strength. We first demonstrate how this can be used to predict the system's temperature after the quench from equilibrium properties at the pre-quench temperature. For a thermalizing post-quench system, it …

Colored Petri Nets are Lax Double Functors
Jade Master, Joe Moeller
https://arxiv.org/abs/2510.01946 https://arxiv.org/pdf/2510.01946

Colored Petri Nets are Lax Double Functors
We give a characterization of colored Petri nets as lax double functors. Framing colored Petri nets in terms of category theory allows for canonical definitions of various well-known constructions on colored Petri nets. In particular, we show how morphisms of colored Petri nets may be understood as natural transformations. A result from folklore, which we sketch in the appendix, shows that lax double functors are equivalent to functors with codomain their former domain. We use this result to ch…

Sequential quantum processes with group symmetries
Dmitry Grinko, Satoshi Yoshida, Mio Murao, Maris Ozols
https://arxiv.org/abs/2510.07100 https://arxiv.or…

Sequential quantum processes with group symmetries
Symmetry plays a crucial role in the design and analysis of quantum protocols. This result shows a canonical circuit decomposition of a $(G \times H)$-invariant quantum comb for compact groups $G$ and $H$ using the corresponding Clebsch-Gordan transforms, which naturally extends to the $G$-covariant quantum comb. By using this circuit decomposition, we propose a parametrized quantum comb with group symmetry, and derive the optimal quantum comb which transforms an unknown unitary operation $U \i…

Canonical Reduction Systems in Artin-Tits groups of spherical type
Mar\'ia Cumplido, Juan Gonz\'alez-Meneses, Davide Perego
https://arxiv.org/abs/2510.00713 https://

Canonical Reduction Systems in Artin-Tits groups of spherical type
We introduce the canonical reduction system of an element in an Artin-Tits group of spherical type, which generalizes the similar notion for braids (and mapping classes) introduced by Birman, Lubotzky and McCarthy. We show its basic properties, which coincide with those satisfied in braid groups, and we provide an algorithm to compute it. We improve the algorithm in the case of braid groups, and discuss its complexity in this case. As a necessary result for obtaining the general algorithm, we p…

Secant loci on moduli of Prym varieties
Gavril Farkas, Margherita Lelli-Chiesa
https://arxiv.org/abs/2509.26118 https://arxiv.org/pdf/2509.26118

Secant loci on moduli of Prym varieties
We present a Prym analogue of Lazarsfeld's result that curves on general polarized K3 surfaces verify the Brill-Noether Theorem, or equivalently, that their canonical embedding has no unexpected secants. We show that the Prym-canonical embedding of a curve on a general Nikulin surface (both of standard and non-standard types) has no unexpected secants. We then explain how these geometric facts suffice to determine the class of the universal difference divisor on the moduli space of stable Prym …

Quadrangulations and the Lov\'asz complex
Carmen Arana, Mat\v{e}j Stehl\'ik
https://arxiv.org/abs/2510.03698 https://arxiv.org/pdf/2510.03698

Quadrangulations and the Lovász complex
The Lovász complex $L(G)$ of a graph $G$ is a deformation retract of its neighborhood complex, equipped with a canonical $Z_2$-action. We show that, under mild assumptions, $L(G)$ is homeomorphic to a surface if and only if $G$ is a non-bipartite quadrangulation of the orbit space $L(G)/Z_2$ in which every $4$-cycle is facial. This yields a classification of the Lovász complexes of all such quadrangulations. As an application, we contextualize a result of Archdeacon \emph{et al.}\ and Mohar a…

Functor categories, Recollements, Triangular Matrix category
M. L. S. Sandoval-Miranda, V. Santiago-Vargas, E. O. Velasco-P\'aez
https://arxiv.org/abs/2509.18290 https://

Functor categories, Recollements, Triangular Matrix category
In this paper we study triangular matrix categories using the theory of recollements of abelian categories. Given a triangular matrix category we construct two canonical recollements. We show that if certain funtors of these recollements are exact then the category appearing in the middle term is actually a triangular matrix category. This result is a generalization of one given by Liping Li in \cite{LipingLi}. We also show that if $\mathrm{Mod}(\mathcal{C})$ admits a nontrivial torsion pair by…

Abundance anomalies in low mass field mergers as evidence of a merger origin for the second generation stars in globular clusters
Valery Kravtsov (Sternberg Astronomical Institute, Lomonosov Moscow State University, Russia), Sami Dib (Max Planck Institute for Astronomy, Germany), Francisco A. Calderon (Departamento de Fisica, Unuversidad Catolica del Norte, Chile)

Abundance anomalies in low mass field mergers as evidence of a merger origin for the second generation stars in globular clusters
The canonical formation of second-generation (G2) stars in globular clusters (GCs) from gas enriched and ejected by G1 (primordial) polluters faces substantial challenges, i.e. (i) a mass-budget problem and (ii) uncertainty in the source(s) of the abundance anomaly of light elements (AALE) in G2 stars. The merger of G1 low-mass main-sequence (MS) binaries can overcome (i), but its ability to result in AALE is omitted. We provide evidence of the merger process to explain AALE by relying on highl…