On the values of unipotent characters in bad characteristic

2017/11/15 by Geck, Meinolf
#20C33 #20G40 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1711.05778

Abstract

Let G(q) be a Chevalley group over a finite field F_q. By Lusztig's and Shoji's work, the problem of computing the values of the unipotent characters of G(q) is solved, in principle, by the theory of character sheaves; one issue in this solution is the determination of certain scalars relating two types of class functions on G(q). We show that this issue can be reduced to the case where q is a prime, which opens the way to use computer algebra methods. Here, and in a sequel to this article, we use this approach to solve a number of cases in groups of exceptional type which seemed hitherto out of reach.

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