Related papers: On defining characteristic representations of fini…
In this paper we study the complete reducibility of representations of infinite-dimensional Lie algebras from the perspective of the representation theory of vertex algebras.
We study the representation theory of quantizations of Gieseker moduli spaces. We describe the categories of finite dimensional representations for all parameters and categories O for special values of parameters. We find the values of…
We prove a Mackey formula for representations of finite groups of Lie type, in the case where the groups come from disconnected reductive groups.
We present in detail the classification of the finite dimensional irreducible representations of the super Yangian associated with the Lie superalgebra $gl(1|1)$.
We examine various consequences of the existence of exceptional representations of an irreducible Weyl group. (These are notes from a talk in the MIT Lie groups seminar.)
Let O be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite O-module M of rank two. The main emphasis is on the interaction between…
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.
We describe the group of continuous automorphisms of all simple infinite-dimensional linearly compact Lie superalgebras and use it in order to classify F-forms of these superalgebras over any field F of characteristic zero.
The main result of this paper is the classification of the real irreducible representations of compact Lie groups with vanishing homogeneity rank.
Arithmetical properties of a finite group are properties of the group which are defined by its arithmetical parameters such as the order of the group, the element orders and so on. In this paper, we discuss a number of results on…
We study the complex irreducible representations of special linear, symplectic, orthogonal and unitary groups over principal ideal local rings of length two. We construct a canonical correspondence between the irreducible representations of…
It is generally believed (and for the most part is probably true) that Lie theory, in contrast to the characteristic zero case, is insufficient to tackle the representation theory of algebraic groups over prime characteristic fields.…
We study the asymptotics of representations of a fixed compact Lie group. We prove that the limit behavior of a sequence of such representations can be described in terms of certain random matrices; in particular operations on…
The special linear representation of a compact Lie group G is a kind of linear representation of compact Lie group G with special properties. It is possible to define the integral of linear representation and extend this concept to special…
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…
In this article, we classify disconnected reductive groups over an algebraically closed field with a few caveats. Internal parts of our result are both a classification of finite groups and a classification of integral representations of a…
A parametrization of irreducible unitary representations associated with the regular adjoint orbits of a hyperspecial compact subgroup of a reductive group over a non-dyadic non-archimedean local filed is presented. The parametrization is…
We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…
This note presents a procedure to determine the reduction of the irreducible and the induced characters of the symmetric group in terms of the irreducible and induced characters of the hyperoctahedral group Key Words: Symmetric Group,…