The Largest Irreducible Representations of Simple Groups

Abstract

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.

34 pages

Cited by in corpus (7)

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• Character bounds for regular semisimple elements and asymptotic results on Thompson's conjecture
• Finite groups with an irreducible character of large degree