Related papers: Representation Theory of Polyadic Groups
Some question about representations of $p$-adic groups are discussed.
We prove that there is a one-one correspondence between sets of irreducible representations of a polyadic group and its Post's cover. Using this correspondence, we generalize some well-known properties of irreducible characters in finite…
In this expository paper we review some recent results about representations of Kac-Moody groups. We sketch the construction of these groups. If practical, we present the ideas behind the proofs of theorems. At the end we pose open…
We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify…
Polyadic systems and their representations are reviewed and a classification of general polyadic systems is presented. A new multiplace generalization of associativity preserving homomorphisms, a 'heteromorphism' which connects polyadic…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
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…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
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…
An axiomatic approach to the representation theory of Coxeter groups and their Hecke algebras was presented in [1]. Combinatorial aspects of this construction are studied in this paper. In particular, the symmetric group case is…
We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…
The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…
Using a unified method, we determine the structure of automorphisms and representations of arbitrary polyadic groups. More precisely, for a polyadic group $(G, f)=der_{\theta, b}(G, \cdot)$, we obtain a complete description of automorphisms…
In the first part of this paper we try to explain to a general mathematical audience some of the remarkable web of conjectures linking representations of Galois groups with algebraic geometry, complex analysis and discrete subgroups of Lie…
In this review, we have reached from the most basic definitions in the theory of groups, group structures, etc. to representation theory and irreducible representations of the Poincar'e group. Also, we tried to get a more comprehensible…
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.
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
In this paper we study some algebraic properties of the rack structure as well as the representation theory of it, following the ideas given by M. Elhamdadi and E. M. Moutuou in \cite{Elhamdadi}. We establish a correspondence between the…
This paper studies unitary representations with Dirac cohomology for complex groups, in particular relations to unipotent representations
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.