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We extend the decomposition conjecture to 2d quantum field theories with a gauged $\text{Rep}(H)$ symmetry category for $H$ a finite-dimensional semisimple Hopf algebra with $\text{Rep}(G)$ trivially-acting and $\text{Vec}(\Gamma)$ the…

High Energy Physics - Theory · Physics 2026-02-27 Alonso Perez-Lona

We study the structure of the indecomposable direct summands of tensor products of two restricted simple $SL_3(K)$-modules, where $K$ is an algebraically closed field of characteristic $p \geq 5$. We give a characteristic-free algorithm for…

Representation Theory · Mathematics 2014-09-25 C. Bowman , S. R. Doty , S. Martin

We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…

Commutative Algebra · Mathematics 2022-02-15 Justin Chen , Yairon Cid-Ruiz

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

Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…

Discrete Mathematics · Computer Science 2021-01-25 Michel Habib , Lalla Mouatadid , Eric Sopena , Mengchuan Zou

We show that the stable module $\infty$-category of a finite group $G$ decomposes in three different ways as a limit of the stable module $\infty$-categories of certain subgroups of $G$. Analogously to Dwyer's terminology for homology…

Representation Theory · Mathematics 2020-09-25 Joshua Hunt

In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…

Representation Theory · Mathematics 2025-12-19 Morton E. Harris

Let $\Pi$ be a convex decomposition of a set $P$ of $n\geq 3$ points in general position in the plane. If $\Pi$ consists of more than one polygon, then either $\Pi$ contains a deletable edge or $\Pi$ contains a contractible edge.

Combinatorics · Mathematics 2017-09-19 Ferran Hurtado , Eduardo Rivera-Campo

Recently, the first two authors have defined a Z-grading on group algebras of symmetric groups and more generally on the cyclotomic Hecke algebras of type G(l,1,d). In this paper we explain how to grade Specht modules over these algebras.

Representation Theory · Mathematics 2011-10-28 Jonathan Brundan , Alexander Kleshchev , Weiqiang Wang

This paper shows that certain decomposition numbers for the Hecke algebras and q-Schur algebras at different roots of unity in characteristic zero are equal. To prove our results we first establish the corresponding theorem for the…

Representation Theory · Mathematics 2009-09-25 Gordon James , Andrew Mathas

This article introduces the Hartwig-Spindelb\"{o}ck decomposition of dual complex matrices. We provide representations of some generalized inverses using this decomposition. Further, several characterizations are established for a complex…

Rings and Algebras · Mathematics 2024-10-30 Aaisha Be , Debasisha Mishra

Using Lusztig's geometric classification, we find the reducibility points of a standard module for the affine Hecke algebra, in the case when the inducing data is generic. This recovers the known result of Muic-Shahidi for representations…

Representation Theory · Mathematics 2012-04-23 Dan Barbasch , Dan Ciubotaru

We develop a combinatorial and order-theoretic framework for shuffles, understood as ordered concatenations of indexed families of sequences that induce total orders on the natural numbers. Motivated by the classical \v{S}arkovski\u{i}…

Combinatorics · Mathematics 2026-02-03 João Dias , Bruno Dinis , Carlos Correia Ramos

We give explicit formulas to compute most of the decomposition numbers of reductions modulo 2 of irreducible spin representations of symmetric groups indexed by partitions with at most 2 parts. In many of the still open cases small upper…

Representation Theory · Mathematics 2024-02-02 Lucia Morotti

A framework to systematically decouple high order elliptic equations into combination of Poisson-type and Stokes-type equations is developed. The key is to systematically construct the underling commutative diagrams involving the complexes…

Numerical Analysis · Mathematics 2018-07-03 Long Chen , Xuehai Huang

We compute the trace decategorification of the Hecke category for an arbitrary Coxeter group. More generally, we introduce the notion of a strictly object-adapted cellular category and calculate the trace for such categories.

Representation Theory · Mathematics 2015-12-18 Ben Elias , Aaron D. Lauda

By a result of Hemmer, every simple Specht module of a finite symmetric group over a field of odd characteristic is a signed Young module. While Specht modules are parametrized by partitions, indecomposable signed Young modules are…

Representation Theory · Mathematics 2017-01-17 Susanne Danz , Kay Jin Lim

Two new results concerning complements in a semisimple Hopf algebra are proved. They extend some well known results from group theory. The uniqueness of Krull Schmidt Remak type decomposition is proved for semisimple completely reducible…

Rings and Algebras · Mathematics 2012-08-07 Sebastian Burciu

In this paper, we obtain parametrizations of the moduli space of principal bundles over a compact Riemann surface using spaces of Hecke modifications in several cases. We begin with a discussion of Hecke modifications for principal bundles…

Algebraic Geometry · Mathematics 2011-08-24 Michael Lennox Wong

Soit F un corps local non archimedien de caracteristique residuelle p. On designe par R un corps algebriquement clos de caracteristique p et par Q une cloture algebrique du corps des nombres p-adiques. On classifie les modules simples de…

Representation Theory · Mathematics 2007-05-23 Rachel Ollivier
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