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Related papers: Remarks on Nahm sums for symmetrizable matrices

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We associate to every matroid M a polynomial with integer coefficients, which we call the Kazhdan-Lusztig polynomial of M, in analogy with Kazhdan-Lusztig polynomials in representation theory. We conjecture that the coefficients are always…

Combinatorics · Mathematics 2016-07-04 Ben Elias , Nicholas Proudfoot , Max Wakefield

Mirror symmetry suggests unexpected relationships between arithmetic properties of distinct families of algebraic varieties. For example, Wan and others have shown that for some mirror pairs, the number of rational points over a finite…

Number Theory · Mathematics 2024-02-05 Adriana Salerno , Ursula Whitcher

Multiplicative Hitchin systems are analogues of Hitchin's integrable system based on moduli spaces of G-Higgs bundles on a curve C where the Higgs field is group-valued, rather than Lie algebra valued. We discuss the relationship between…

Algebraic Geometry · Mathematics 2021-10-29 Chris Elliott , Vasily Pestun

This survey paper is based on a talk given at the 44th Summer Symposium in Real Analysis in Paris. This line of research was initiated by a question of Haight and Weizs\"aker concerning almost everywhere convergence properties of series of…

Classical Analysis and ODEs · Mathematics 2022-09-27 Zoltán Buczolich

Let $G$ be a finite group and let $k$ be an algebraically closed field of characteristic $2$ and let $M$ be an indecomposable $kG$-module which affords a non-degenerate $G$-invariant symmetric bilinear form. We introduce the symmetric…

Representation Theory · Mathematics 2016-04-21 John C. Murray

Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generalization of extension and gauging group symmetries to category…

Quantum Algebra · Mathematics 2019-11-05 Shawn X. Cui , Modjtaba Shokrian Zini , Zhenghan Wang

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

Representation Theory · Mathematics 2020-12-09 Olivier Brunat , Jean-Baptiste Gramain , Nicolas Jacon

We propose a method to unify various stability results about symmetric ideals in polynomial rings by stratifying related derived categories. We execute this idea for chains of $GL_n$-equivariant modules over an infinite field $k$ of…

Commutative Algebra · Mathematics 2024-07-24 Karthik Ganapathy

We prove that Nahm transform for integrable connections with a finite number of regular singularities and an irregular singularity of rank 1 on the Riemann sphere is equivalent -- up to considering integrable connections as holonomic…

Algebraic Geometry · Mathematics 2012-08-06 Szilard Szabo

We study modular theory in hyperfinite von Neumann algebras, i.e. in those of type II or type III, from the viewpoint of a subregion charge sector decomposition. We address this symmetry resolution by considering infinite tensor products of…

High Energy Physics - Theory · Physics 2025-10-06 Giuseppe Di Giulio , Moritz Dorband , Johanna Erdmenger , Henri Scheppach

We verify a finiteness conjecture of Feit on sources of simple modules over group algebras for various classes of finite groups related to the symmetric groups.

Representation Theory · Mathematics 2011-12-21 Susanne Danz , Jürgen Müller

This paper studies the vertices, in the sense defined by J. A. Green, of Specht modules for symmetric groups. The main theorem gives, for each indecomposable non-projective Specht module, a large subgroup contained in one of its vertices. A…

Representation Theory · Mathematics 2009-07-07 Mark Wildon

Some spontaneously broken gauge theories with unbroken non-Abelian gauge groups contain massless magnetic monopoles that are realized classically as clouds of non-Abelian field surrounding one or more massive monopoles. We use moduli space…

High Energy Physics - Theory · Physics 2009-11-06 Christopher M. Miller , Erick J. Weinberg

We consider symmetric (under the action of products of finite symmetric groups) real algebraic varieties and semi-algebraic sets, as well as symmetric complex varieties in affine and projective spaces, defined by polynomials of degrees…

Algebraic Geometry · Mathematics 2017-05-01 Saugata Basu , Cordian Riener

We construct isomorphisms between spaces of vector-valued modular forms for the dual Weil representation and certain spaces of scalar-valued modular forms in the case that the underlying finite quadratic module $A$ has order $p$ or $2p$,…

Number Theory · Mathematics 2020-06-19 Markus Schwagenscheidt , Brandon Williams

We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices as stochastic transition matrices of random…

Combinatorics · Mathematics 2017-12-27 Lin Jiu , Diane Yahui Shi

We study the indecomposable summands of the permutation module obtained by inducing the trivial $\mathbb{F}(S_a\wr S_n)$-module to the full symmetric group $S_{an}$ for any field $\mathbb{F}$ of odd prime characteristic $p$ such that…

Representation Theory · Mathematics 2014-04-18 Eugenio Giannelli

We introduce $q$-analogues of uniform matroids, which we call $q$-niform matroids. While uniform matroids admit actions of symmetric groups, $q$-niform matroids admit actions of finite general linear groups. We show that the equivariant…

Combinatorics · Mathematics 2018-09-05 Nicholas Proudfoot

We prove a result that relates the number of homomorphisms from the fundamental group of a compact nonorientable surface to a finite group $G$, where conjugacy classes of the boundary components of the surface must map to prescribed…

Group Theory · Mathematics 2025-02-19 Michael R. Klug

In this paper we investigate the arithmetic aspects of the theory of $\mathcal{E}_K^\dagger$-valued rigid cohomology introduced and studied in [11,12]. In particular we show that these cohomology groups have compatible connections and…

Number Theory · Mathematics 2015-03-10 Christopher Lazda , Ambrus Pál
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