Related papers: Rational representations and permutation represent…

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…

We consider a variant of the Zak transform for a finite group $G$ with respect to a fixed abelian subgroup $H$, and demonstrate a relationship with representations of $G$ induced from characters of $H$. We also show how the Zak transform…

Extending earlier work of Guralnick and of Cai and Zhang, we classify the almost simple groups which have transitive permutation representations of prime power degree $p^k$, and those which have $p$-complements (stabilisers of order coprime…

Preface (A.Vershik) - about these texts (3.); I.Interpolation between inductive and projective limits of finite groups with applicatons to linear groups over finite fields; II.The characters of the groups of almost triangle matrices over…

Over a field of characteristic 0, every ring of invariants of a finite group is Cohen-Macaulay. This is not true for fields of positive characteristic. We consider permutation representations and their invariant rings over fields…

An isomorphism between the group ring of a finite group and a ring of certain block diagonal matrices is established. The group ring $RG$ of a finite group $G$ is isomorphic to the set of {\em group ring matrices} over $R$. It is shown that…

In \cite{DFW} and \cite{Fu07}, little $q$-Schur algebras were introduced as homomorphic images of the infinitesimal quantum groups. In this paper, we will investigate representations of these algebras. We will classify simple modules for…

We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…

This text is an extended version of the lecture notes for a course on representation theory of finite groups that was given by the authors during several years for graduate and postgraduate students of Novosibirsk State University and…

We prove that, up to adding a complement, every modular representation of a finite group admits a finite resolution by permutation modules.

We prove that if $G$ is a finite simple group, then all irreducible complex representations of $G$ by be realized over the real numbers if and only if every element of $G$ may be written as a product of two involutions in $G$. This follows…

This paper uses tools in group theory and symbolic computing to give a classification of the representations of finite groups with order lower than 9 that can be derived from the study of local reversible-equivariant vector fields in…

A quasi-semiregular element in a permutation group is an element that has a unique fixed point and acts semiregularly on the remaining points. Such elements were first studied in the context of automorphisms of graphs and occur naturally in…

The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between…

The concept of $S$-characters of finite groups was introduced by Zhmud' as a generalisation of transitive permutation characters. Any non-trivial $S$-character takes a zero value on some group element. By a deep result depending on the…

Let ${\mathbb{G}}$ be a simply connected ${\mathbb{Z}}_\ell$-spets, let $q$ be a prime power, prime to $\ell$ and let $S$ be the underlying Sylow $\ell$-subgroup. Firstly, motivated by known formulae for values of Deligne-Lusztig characters…

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for these forms. Through their connection to quadratic forms, we…

For a finite group $G$, we denote by $\mu(G)$ and $c(G),$ the minimal degree of faithful permutation representation of $G$ and the minimal degree of faithful representation of $G$ by quasi-permutation matrices over the complex field…

We determine subnormalisers of semisimple elements of prime power order in finite quasi-simple groups of Lie type. For this, we determine the maximal overgroups of normalisers of Sylow tori. This is motivated by the recent character…