On semisimple classes and semisimple characters in finite reductive groups

Details On semisimple classes and semisimple characters in finite reductive groups On semisimple classes and semisimple characters in finite reductive groups

2010-03-17

arxiv.org/abs/1003.3283v1

Mathematics

Representation Theory

Scientific paper

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.

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