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Computing Green functions in small characteristic. (English) Zbl 07239064
Summary: Let $$G(q)$$ be a finite group of Lie type over a field with $$q$$ elements, where $$q$$ is a prime power. The Green functions of $$G(q)$$, as defined by Deligne and Lusztig, are known in almost all cases by work of Beynon-Spaltenstein, Lusztig und Shoji. Open cases exist for groups of exceptional type $${}^2E_6, E_7, E_8$$ in small characteristics. We propose a general method for dealing with these cases, which proceeds by a reduction to the case where $$q$$ is a prime and then uses computer algebra techniques. In this way, all open cases in type $${}^2E_6, E_7$$ are solved, as well as at least one particular open case in type $$E_8$$.

##### MSC:
 20C33 Representations of finite groups of Lie type 20G40 Linear algebraic groups over finite fields
GAP; CHEVIE
Full Text:
##### References:
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