Related papers: Character theory at a torsion element

In this article we try to explore the relation between real conjugacy classes and real characters of finite groups at more refined level. This refinement is in terms of properties of groups such as strong reality and total orthogonality. In…

Some general connections between martingales and character ratios of finite groups are developed. As an application we sharpen the convergence rate in a central limit theorem for the character ratio of a random representation of the…

The Divisibility Graph of a finite group $G$ has vertex set the set of conjugacy class lengths of non-central elements in $G$ and two vertices are connected by an edge if one divides the other. We determine the connected components of the…

This survey article is an introduction to some of Lusztig's work on the character theory of a finite group of Lie type $G(F_q)$, where $q$ is a power of a prime~$p$. It is partly based on two series of lectures given at the Centre Bernoulli…

The goal of this expository article, based on a lecture I gave at the 2016 ICRA, is to explain some recent applications of "categorical symmetries" in topology and algebraic geometry with an eye toward twisted commutative algebras as a…

For a finite group $G$ we investigate the smallest positive integer $e(G)$ such that the map sending $g\in G$ to $e(G)|G:C_G(g)|$ is a generalized character of $G$. It turns out that $e(G)$ is strongly influenced by local data, but behaves…

This paper is a continuation of [GLT], which develops a level theory and establishes strong character bounds for finite simple groups of linear and unitary type in the case that the centralizer of the element has small order compared to…

Character measure is a probability measure on irreducible representations of a semisimple Lie algebra. It appears from the decomposition into irreducibles of tensor power of a fundamental representation. In this paper we calculate the…

For a torsion unit $u$ of the integral group ring $\mathbb{Z} G$ of a finite group $G$, and a prime $p$ which does not divide the order of $u$ (but the order of $G$), a relation between the partial augmentations of $u$ on the $p$-regular…

Let $\mathcal{A}$ be an abelian length category containing a $d$-cluster tilting subcategory $\mathcal{M}$. We prove that a subcategory of $\mathcal{M}$ is a $d$-torsion class if and only if it is closed under $d$-extensions and…

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…

We investigate a beautiful conjecture of T. Wilde on character values and element orders of finite groups. We reduce it to a statement on nearly simple groups that can be checked ``prime by prime". For these groups, we show that a strong…

We review some recent results on properties of tensor product and fusion coefficients under complex conjugation of one of the factors. Some of these results have been proven, some others are conjectures awaiting a proof, one of them…

This paper is concerned with the representation theory of finite groups. According to Robinson, the truth of certain variants of Alperin's weight conjecture on the $p$-blocks of a finite group would imply some arithmetical conditions on the…

Let $\Lambda$ be a finite-dimensional associative algebra. The torsion classes of $mod\, \Lambda$ form a lattice under containment, denoted by $tors\, \Lambda$. In this paper, we characterize the cover relations in $tors\, \Lambda$ by…

Let A be a character sheaf on a reductive connected group G over an algebraically closed field. Assuming that the characteristic is not bad, we show that for certain conjugacy classes D in G the restriction of A to D is a local system up to…

Given a finite group G, let cd(G) denote the set of degrees of the irreducible complex characters of G. The character degree graph of G is defined as the simple undirected graph whose vertices are the prime divisors of the numbers in cd(G),…

In representation theory of finite groups an important role is played by irreducible characters of p-defect 0, for a prime p dividing the group order. These are exactly those vanishing at the p-singular elements. In this paper we generalize…

Exploiting particular features of classical groups, simple constructions are given for the irreducible constituents of the tensor square of the adjoint modules and the leading terms in higher tensor powers. This provides an independent…

This article is concerned with the relative McKay conjecture for finite reductive groups. Let G be a connected reductive group defined over the finite field F_q of characteristic p>0 with corresponding Frobenius map F. We prove that if the…