相关论文: Two geometric character formulas for reductive Lie…

The purpose of this paper is to begin an exploration of connections between the Baum-Connes conjecture in operator $\K$-theory and the geometric representation theory of reductive Lie groups. Our initial goal is very modest, and we shall…

In this paper I present a new and unified method of proving character formulas for discrete series representations of connected Lie groups by applying a Chern character-type construction to the matrix factorizations of [FT] and [FHT3]. In…

I calculate characters of certain representations of loop groups based on non simply connected Lie groups. This gives a generalization of the Kac-Weyl character formula.

This article provides a geometric bridge between two entirely different character formulas for reductive Lie groups and answers the question posed by W.Schmid in [Sch]. A corresponding problem in the compact group setting was solved by…

In this paper we obtain a decomposition formula of the uniform projection of the Weil character of a finite reductive dual pair consisting of a symplectic group and an even orthogonal group. This is the first and major step to give an…

It is known that characters of irreducible representations of finite Lie algebras can be obtained using theWeyl character formula including Weyl group summations which make actual calculations almost impossible except for a few Lie algebras…

We give the generalized Atiyah-Schmid formula for projective tempered representations. Then we prove the Atiyah-Schmid formula for arithmetic subgroups of real reductive groups.

Let G be a possibly disconnected reductive real Lie group. In this paper, I parametrize the set of irreductible tempered characters of G. I then describe these characters using certain ``Kirillov's formulas,'' based on the descent method…

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…

In this paper we study the complex representations of reductive groups over local non-Archimedean fields. We use the building of the reductive group to give upper-bounds for the absolute value of the character of an admissible…

The goal of this diploma thesis is to give a detailed description of Kirillov's Orbit Method for the case of compact connected Lie groups. The theory of Kirillov aims at finding all irreducible unitary representations of a given Lie group…

These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on Lusztig's character formula and geometric representation theory. They are based on the…

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations…

We establish several characterizations of Anosov representations of word hyperbolic groups into real reductive Lie groups, in terms of a Cartan projection or Lyapunov projection of the Lie group. Using a properness criterion of Benoist and…

In this survey paper, we present the broad outlines of the proof of a character formula for tilting representations of reductive algebraic groups in positive characteristic, obtained partly in collaboration with several other authors. A…

The decomposition of representations of compact classical Lie groups into representations of finite subgroups is discussed. A Mathematica package is presented that can be used to compute these branching rules using the Weyl character…

We develop an approach to the character theory of certain classes of finite and profinite groups based on the construction of a Lie algebra associated to such a group, but without making use of the notion of a polarization which is central…

Harish-Chandra classified discrete series representations of real semisimple Lie groups by describing their characters as tempered distributions with an explicit formula on the elliptic set. His approach was inspired by Weyl's proof of the…

We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu's construction from data satisfying a certain compactness condition. Each character is…