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On the values of unipotent characters in bad characteristic. (English) Zbl 07083123
Summary: 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.

MSC:
20C33 Representations of finite groups of Lie type
20G40 Linear algebraic groups over finite fields
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