Related papers: Representations of finite groups
This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions are defined for topological groups, but a…
This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first order theory of finite groups. The focus is on concepts from stability theory…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
Topological full groups originated from the theory of topological dynamical systems and have been having considerable impact on group theory in recent years. This text represents an introduction/survey on topological full groups. After…
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
This paper is a historical and mathematical review of the book, "The q-theory of Finite Semigroups" by John Rhodes and Benjamin Steinberg.
Let $\mathbf{G}$ be a connected reductive group over a finite field $\mathbb{F}_q$ of characteristic $p > 0$. In this paper, we study a category which we call Deligne--Lusztig category $\mathcal{O}$ and whose definition is similar to…
We will explore the nature of when certain finite groups have an equal covering, and when finite groups do not. Not to be confused with the concept of a cover group, a covering of a group is a collection of proper subgroups whose…
This is the first installment of a book on combinatorial and geometric group theory from the topological point of view. This is a classical subject. The installment contains Chapters 1, 3 and 4, and there are nine chapters in total: 1.…
Let W be a Weyl group. In my 1984 book a group was attached to any special representation of W using the theory of Springer representations. In this paper we give a new definition of this group which is purely algebraic (no use of geometry…
A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.
The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged…
Recent results on finite open group transformations are reviewed.
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…
The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…
This paper deals with the number of subgroups of a given exponent in a finite abelian group. Explicit formulas are obtained in the case of rank two and rank three abelian groups. An asymptotic formula is also presented.
Much has been written on reciprocity laws in number theory and their connections with group representations. In this paper we explore more on these connections. We prove a "reciprocity Law" for certain specific representations of semidirect…
We attempt to survey the field of combinatorial representation theory, describe the main results and main questions and give an update of its current status. We give a personal viewpoint on the field, while remaining aware that there is…
The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…