Olivier Brunat
On semisimple classes and semisimple characters in finite reductive groups.
Thu, 03/18/2010 - 16:01 — SomNambulAuthors: Olivier Brunat
Subjects: Representation Theory
AbstractIn 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.On equivariant bijections relative to the defining characteristic.
Tue, 09/08/2009 - 12:16 — SomNambulAuthors: Olivier Brunat, Frank Himstedt
Subjects: Representation Theory
AbstractThis paper is a contribution to the general program introduced by Isaacs,
Malle and Navarro to prove the McKay conjecture in the representation theory of
finite groups. We develop new methods for dealing with simple groups of Lie
type in the defining characteristic case. Using a general argument based on the
representation theory of connected reductive groups with disconnected center,
we show that the inductive McKay condition holds if the Schur multiplier of the
simple group has order 2.
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