On the values of unipotent characters in bad characteristic

Geck, Meinolf

Rendiconti del Seminario Matematico della Università di Padova, Tome 141 (2019), pp. 37-63.

Let $G\left(q\right)$ 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 $G\left(q\right)$ 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 $G\left(q\right)$. 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.

Classification : 20, 00
Mots clés : Finite groups of Lie type, unipotent characters, character sheaves