12 research outputs found
The Largest Irreducible Representations of Simple Groups
Answering a question of I. M. Isaacs, we show that the largest degree of
irreducible complex representations of any finite non-abelian simple group can
be bounded in terms of the smaller degrees. We also study the asymptotic
behavior of this largest degree for finite groups of Lie type. Moreover, we
show that for groups of Lie type, the Steinberg character has largest degree
among all unipotent characters.Comment: 34 page
Conjectures of Alperin and Broue for 2-blocks with elementary abelian defect groups of order 8
Using the classification of finite simple groups we prove Alperin's weight
conjecture and the character theoretic version of Broue's abelian defect group
conjecture for 2-blocks of finite groups with an elementary abelian defect
group of order 8.Comment: 40 page