Related papers: Small Representations of Finite Classical Groups

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

Finite-state transducers give efficient representations of many Natural Language phenomena. They allow to account for complex lexicon restrictions encountered, without involving the use of a large set of complex rules difficult to analyze.…

An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…

We study the finite-dimensional continuous complex representations of $\mathrm{SL}_2$ over the ring of integers of non-Archimedean local fields of even residual characteristic. We prove that for characteristic two, the abscissa of…

We investigate the question which Q-valued characters and characters of Q-representations of finite groups are Z-linear combinations of permutation characters. This question is known to reduce to that for quasi-elementary groups, and we…

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…

We study the representation growth of alternating and symmetric groups in positive characteristic and restricted representation growth for the finite groups of Lie type. We show that the the number of representations of dimension at most n…

We develop a theory of levels for irreducible representations of symmetric groups of degree $n$ analogous to the theory of levels for finite classical groups. A key property of level is that the level of a character, provided it is not too…

In this paper we study the Gan-Gross-Prasad problem for finite classical groups. Our results provide complete answers for unipotent representations, and we obtain the explicit branching laws for these representations. Moreover, for…

We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie type.

In this work, we establish a relationship between the sum of irreducible character degrees and the number of twisted involutions associated with the automorphisms of a finite group. We develop algorithmic frameworks for evaluating these…

Motivated by analogous results for the symmetric group and compact Lie groups, we study the distribution of the number of fixed vectors of a random element of a finite classical group. We determine the limiting moments of these…

In this article, we classify disconnected reductive groups over an algebraically closed field with a few caveats. Internal parts of our result are both a classification of finite groups and a classification of integral representations of a…

The concept of a C-approximable group, for a class of finite groups C, is a common generalization of the concepts of a sofic, weakly sofic, and linear sofic group. Glebsky raised the question whether all groups are approximable by finite…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

In this series of papers, we investigate properties of a finite group which are determined by its low degree irreducible representations over a number field $F$, i.e. its representations on matrix rings $\operatorname{M}_n(D)$ with $n \leq…

This paper is concerned with integrals which integrands are the monomials of matrix elements of irreducible representations of classical groups. Based on analysis on Young tableaux, we discuss some related duality theorems and compute the…

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…

We give a simple formula for the essential dimension of a finite pseudo-reflection group at a prime p and determine the absolute essential dimension for most irreducible pseudo-reflection groups. We also study the "poor man's essential…