相关论文: A character formula for certain representations of…

We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.

Lie groups with two different root lengths allow two mixed sign homomorphisms on their corresponding Weyl groups, which in turn give rise to two families of hybrid Weyl group orbit functions and characters. In this paper we extend the ideas…

In this paper we compute the K-theory (algebraic and topological) and entire periodic cyclic homology for compact quantum groups, define Chern characters between them and show that the Chern characters in both topological and algebraic…

This paper concerns character sheaves of connected reductive algebraic groups defined over non-Archimedean local fields and their relation with characters of smooth representations. Although character sheaves were devised with characters of…

In 2015, the author proved combinatorially character formulas expressing sums of the (formal) dimensions of irreducible representations of symplectic groups, refining some works of Nekrasov and Okounkov, Han, King, and Westbury. In this…

We proved a new Siegel-Weil formula for orthogonal and symplectic groups, which will be used later to prove a generalization of Siegel-Weil formula for loop groups.

The formulas for subregular characters of the unitriangular Lie group are obtained. The supports of regular and subregular characters are described in terms of the orbit method.

We provide detailed calculations for the classification of representations of compact simple Lie groups with non-empty boundary in the orbit space, first announced in a previous paper [arXiv:2112.00513] by the same authors.

In this note a combinatorial formula related to the symmetric group is generalized to an arbitrary finite Weyl group.

These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions…

We give closed formulae for the q-characters of the fundamental representations of the quantum loop algebra of a classical Lie algebra in terms of a family of partitions satisfying some simple properties. We also give the multiplicities of…

We define the character of a group representation in a 2-category C. For linear C, this notion yields a Hopkins-Kuhn-Ravenel type character theory defined on pairs of commuting elements of the group. We discuss some examples and prove a…

The present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum…

We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of…

We use character theory of finite groups of Lie type to establish new results on representation varieties of Fuchsian groups, and also on probabilistic generation of groups of Lie type.

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…

We initiate the representation theory of restricted Lie superalgebras over an algebraically closed field of characteristic p>2. A superalgebra generalization of the celebrated Kac-Weisfeiler Conjecture is formulated, which exhibits a…

Let $G_\cpl$ be a connected complex reductive Lie group, and $G$ be a real form. Let $(\pi,V)$ be a finite-dimensional irreducible representation of $G$. Assume $(\pi,V)$ admits a $G$ invariant hermitian form. {In…

We give an explicit expression of the normalized characters of the symmetric group in terms of the contents of the partition labelling the representation.

Let V be a symplectic vector space over a finite or local field. We compute the character of the Weil representation of the metaplectic group Mp(V). The final formulas are overtly free of choices (e.g. they do not involve the usual choice…