The Largest Irreducible Representations of Simple Groups

Details The Largest Irreducible Representations of Simple Groups The Largest Irreducible Representations of Simple Groups

2010-10-27

arxiv.org/abs/1010.5628v1

Mathematics

Representation Theory

34 pages

Scientific paper

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.

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