Rendiconti del Seminario Matematico della Università di Padova
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On the values of unipotent characters in bad characteristicMeinolf Geck (1) Universität Stuttgart, Germany
Let $G(q)$ be a Chevalley group over a finite field $\mathbb F_q$. 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.
Keywords: Finite groups of Lie type, unipotent characters, character sheaves
Geck Meinolf: On the values of unipotent characters in bad characteristic. Rend. Sem. Mat. Univ. Padova Electronically published on November 20, 2018. doi: 10.4171/RSMUP/14 (to appear in print)