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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
##### Software:
CHEVIE; GAP; GAP Character Table Library; CTblLib
Full Text:
##### References:
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