Related papers: Representations of finite groups
This article examines lower bounds for the representation growth of finitely generated (particularly profinite and pro-p) groups. It also considers the related question of understanding the maximal multiplicities of character degrees in…
The corepresentation theory of continuous groups is presented without the assumption that the subgroup $G$ of the group with antilinear operations is unitary. The formulas of the corepresentation theory with unitary groups $G$ can be…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all…
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.
We solve an elementary number theory problem on sums of fractional parts, using methods from group theory. We apply our result to deduce the finiteness of certain monodromy representations.
This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.
The Klein group contains only four elements. Nevertheless this little group contains a number of remarkable entry points to current highways of modern representation theory of groups. In this paper, we shall describe all possible ways in…
We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.
The main results in this thesis deal with the representation growth of certain classes of groups. In chapter $1$ we present the required preliminary theory. In chapter $2$ we introduce the Congruence Subgroup Problem for an algebraic group…
The concept of quantum representation of finite groups (QRFG) has been a fundamental aspect of quantum computing for quite some time, playing a role in every corner, from elementary quantum logic gates to the famous Shor's and Grover's…
In this paper we study the Gan-Gross-Prasad problem for unitary groups over finite fields. Our results provide complete answers for unipotent representations, and we obtain the explicit branching of these representations.
The representation theory (idempotents, quivers, Cartan invariants and Loewy series) of the higher order unital peak algebras is investigated. On the way, we obtain new interpretations and generating functions for the idempotents of descent…
Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…
According to Letourmy and Vendramin, a representation of a skew brace is a pair of representations on the same vector space, one for the additive group and the other for the multiplicative group, that satisfies a certain compatibility…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
We describe those unipotent representations of a finite group of Lie type which are defined over the rational numbers.
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…
This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of…