Related papers: On defining characteristic representations of fini…
In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…
We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…
In this paper the author finds explicitly all finite-dimensional irreducible representations of a series of finite permutation groups that are homomorphic images of Artin braid group.
In this note, we formulate an observation that "almost all" irreducible ordinary characters of finite groups of Lie type remain irreducible when restricted to the derived subgroups. To see this, key ingredients are some asymptotic results…
We investigate the action of outer automorphisms of finite groups of Lie type on their irreducible characters. We obtain a definite result for cuspidal characters. As an application we verify the inductive McKay condition for some further…
We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.
For $G$ an algebraic group of type $A_l$ over an algebraically closed field of characteristic $p$, we determine all irreducible rational representations of $G$ in defining characteristic with dimensions $\le (l+1)^s$ for $s = 3, 4$,…
EI-categories are a simultaneous generalisation of finite groups and finite quivers without oriented cycles. It is therefore a natural question to ask for a characterisation of finite representation type. For special classes of…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
A finite EI category is a small category with finitely many morphisms such that every endomorphism is an isomorphism. They include finite groups, finite posets and free categories of finite quivers as special cases. In this paper we…
We characterize the indecomposable injective objects in the category of finitely presented representations of an interval finite quiver.
We introduce an infinite-dimensional affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
We prove that every finite dimensional representation of a finite group over a field of characteristic p admits a finite resolution by p-permutation modules. The proof involves a reformulation in terms of derived categories.
In this series of papers, we investigate properties of a finite group which are determined by its low degree irreducible representations over a number field $F$, i.e. its representations on matrix rings $\operatorname{M}_n(D)$ with $n \leq…
The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on…
We determine the smallest irreducible Brauer characters for finite quasi-simple orthogonal type groups in non-defining characteristic. Under some restrictions on the characteristic we also prove a gap result showing that the next larger…
In the paper we show that any irreducible representation of a finitely generated nilpotent group $G$ over a finitely generated field $F$ of characteristic zero is induced from a primitive representation of some subgroup of $G$.
We construct all finite irreducible modules over Lie conformal superalgebras of type W and S.
We show that irreducible unitary representations of nilpotent super Lie groups can be obtained by induction from a distinguished class of sub super Lie groups. These sub super Lie groups are natural analogues of polarizing subgroups that…