CU Algebraic Lie Theory Seminar

CU Algebraic Lie Theory Seminar
Bounding the Largest Irreducible Character Degree of a Finite Simple Group Shawn Burkett, CU
February 26, 2013 Math 350 2-3pm	Abstract Motivated by the problem of bounding the order of a group with a large character degree, Martin Isaacs predicted that the largest degree among irreducible complex representations of a finite nonabelian simple group could be bounded in terms of the smaller degrees. Using the Jordan decomposition of characters, we answer this question in the affirmative for a few infinite families of finite simple classical groups. We also discuss a recent theorem of Michael Larson, Gunter Malle and Pham Tiep regarding the largest irreducible representations of simple groups, as well as Isaacs's application of this theorem to the problem of bounding the orders of certain groups.

Bounding the Largest Irreducible Character Degree of a Finite Simple Group

Shawn Burkett, CU

February 26, 2013

Math 350

2-3pm

Abstract

Motivated by the problem of bounding the order of a group with a large character degree, Martin Isaacs predicted that the largest degree among irreducible complex representations of a finite nonabelian simple group could be bounded in terms of the smaller degrees. Using the Jordan decomposition of characters, we answer this question in the affirmative for a few infinite families of finite simple classical groups. We also discuss a recent theorem of Michael Larson, Gunter Malle and Pham Tiep regarding the largest irreducible representations of simple groups, as well as Isaacs's application of this theorem to the problem of bounding the orders of certain groups.