On semisimple classes and semisimple characters in finite reductive groups
Representation Theory
2010-03-18 v1 Group Theory
Abstract
In this article, we study the elements with disconnected centralizer in the Brauer complex associated to a simple algebraic group G defined over a finite field with corresponding Frobenius map F and derive the number of F-stable semisimple classes of G with disconnected centralizer when the order of the fundamental group has prime order. We also discuss extendibility of semisimple characters to their inertia group in the full automorphism group. As a consequence, we prove that "twisted" and "untwisted" simple groups of type E_6 are "good" in defining characteristic, which is a contribution to the general program initialized by Isaacs, Malle and Navarro to prove the McKay Conjecture in representation theory of finite groups.
Cite
@article{arxiv.1003.3283,
title = {On semisimple classes and semisimple characters in finite reductive groups},
author = {Olivier Brunat},
journal= {arXiv preprint arXiv:1003.3283},
year = {2010}
}