Related papers: Groups having a faithful irreducible representatio…

In [Frobenius1896] it was shown that many important properties of a finite group could be examined using formulas involving the character ratios of group elements, i.e., the trace of the element acting in a given irreducible representation,…

The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…

Let $G$ be a finite group of Lie type and $\ell$ be a prime which is not equal to the defining characteristic of $G$. In this note we discuss some open problems concerning the $\ell$-modular irreducible representations of $G$. We also…

Let $\mathbb{F}$ be an algebraically closed field and $G$ be an almost quasi-simple group. An important problem in representation theory is to classify the subgroups $H<G$ and $\mathbb{F} G$-modules $L$ such that the restriction…

We study the interplay between different models of the same irreducible representation of the $F$-points of a reductive group over a local field.

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimensio. In particular, we deduce chain conditions for groups, definability results for fields and domains, and show that…

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.

We calculate extensions between certain irreducible admissible representations of p-adic groups.

In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to…

Several recent problems in the representation theory of finite groups require determining whether certain characters of almost simple groups belong to the principal block. Since the values of these characters are not yet known, we employ…

We consider various counting questions for irreducible binomials over finite fields. We use various results from analytic number theory to investigate these questions.

We construct a finitely presented group with undecidable word problem and with Dehn function bounded by a quadratic function on an infinite set of positive integers.

We consider the two-fold problem of representing collective beliefs and aggregating these beliefs. We propose modular, transitive relations for collective beliefs. They allow us to represent conflicting opinions and they have a clear…

Given F a locally compact, non-discrete, non-archimedean field of characteristic different from 2 and R an integral domain such that a non-trivial smooth F-character with values in the multiplicative group of R exists, we construct the…

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…

This report is an account of freely representable groups, which are finite groups admitting linear representations whose only fixed point for a nonidentity element is the zero vector. The standard reference for such groups is Wolf (1967)…

The irreducible decomposition of a unitary representation often contains continuous spectrum when restricted to a non-compact subgroup. The author singles out a nice class of branching problems where each irreducible summand occurs…

We consider an homogeneous action of a finite group on a free linear category over a field in order to prove that the subcategory of invariants is still free. Moreover we show that the representation type is preserved when considering…

In this work, we classify all finite groups such that for every field extension F of \mathbb{Q}, F is the field of values of at most 3 irreducible characters.

A strongly real Beauville group is a Beauville group that defines a real Beauville surface. Here we discuss efforts to find examples of these groups, emphasising on the one extreme finite simple groups and on the other abelian and nilpotent…