Related papers: Representation Theory of Polyadic Groups
This is an overview article on compact Lie groups and their representations, written for the Encyclopedia of Mathematical Physics to be published by Elsevier.
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…
In this article we give an elementary introduction to the representation theory of finite magnetic groups from a purely mathematical point of view. -- En este art\'iculo damos una introducci\'on elemental a la teor\'ia de representaciones…
This article (written in Polish) is aimed for a wide mathematical audience. It is intended as an introductory text concerning problems of the asymptotic theory of symmetric groups.
Motivated by the Langlands program in representation theory, number theory and geometry, the theory of representations of a reductive $p$-adic group over a coefficient ring different from the field of complex numbers has been widely…
We provide a unified treatment of several results concerning full groups of ample groupoids and paradoxical decompositions attached to them. This includes a criterion for the full group of an ample groupoid being amenable as well as…
We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…
A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting…
This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.
This paper is a survey of some of the ways in which the representation theory of the symmetric group has been used in voting theory and game theory. In particular, we use permutation representations that arise from the action of the…
Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…
We define and investigate the concept of the groupoid representation induced by a representation of the isotropy subgroupoid. Groupoids in question are locally compact transitive topological groupoids. We formulate and prove the…
The point of view of these notes on the topic is to bring out the flavour that Representation Theory is an extension of the first course on Group Theory. We also emphasize the importance of the base field. These notes cover completely the…
This is an expository article. We survey some fundamental trends in representation theory of symmetric groups and related objects which became apparent in the last fifteen years. The emphasis is on connections with Lie theory via…
We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.
This is a largely expository paper about how groups arise or are of interest in model theory. Included are the following topics: classifying groups definable in specific structures or theories and the relation to algebraic groups, groups…
We calculate extensions between certain irreducible admissible representations of p-adic groups.
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…
We give a characterization of connected solvable groups in terms of the existence of representations with certain geometric properties. The existence of such representations for the group of upper triangular matrices played an important…
The aim of the present paper is to provide a comprehensive introduction to some algebraic and geometric aspects of real representations of compact Lie groups, as well as some results concerning isotropy strata and restriction of invariants.