Character value estimates for groups of Lie type

Global Character Formulae for Compact Lie Groups

We introduce the concept of a modulator, which leads to a family of character formulae, each generalizing the Kirillov formula. For a suitable choice of modulator, this enables one to understand the Plancherel measure of a compact Lie group as arising from a partition of the identity on the dual of its Lie algebra.

Schauder Estimates on Lie Groups

Weyl’s character formula for non-connected Lie groups and orbital theory for twisted affine Lie algebras

We generalize I. Frenkel’s orbital theory for non twisted affine Lie algebras to the case of twisted affine Lie algebras using a character formula for certain non-connected compact Lie groups.

On the p-defect of character degrees of finite groups of Lie type

This paper is concerned with the representation theory of finite groups. According to Robinson, the truth of certain variants of Alperin’s weight conjecture on the p-blocks of a finite group would imply some arithmetical conditions on the degrees of the irreducible (complex) characters of that group. The purpose of this note is to prove directly that one of these arithmetical conditions is true...

Character Degrees and Random Walks in Finite Groups of Lie Type

In this paper we prove some mainly asymptotic results concerning the irreducible character degrees of .nite groups of Lie type. Applications are given to the study of the mixing time of random walks on these groups, with certain conjugacy classes as generating sets. In various situations we show that the mixing time is 2; this seems to be the .rst determination of an exact bounded mixing time f...