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Green functions of finite Chevalley groups of type \(E_ n (n=6,7,8)\). (English) Zbl 0539.20025
Let k be an algebraic closure of a finite field \(F_ q\). Let G be a connected reductive algebraic group over k defined over \(F_ q\) with Frobenius endomorphism F:\(G\to G\). In the paper Green functions [see P. Deligne and G. Lusztig, Ann. Math., II. Ser. 103, 103-161 (1976; Zbl 0336.20029)] are calculated for the finite group \(G^ F=\{g\in G| \quad F(g)=g\},\) when G is of the type \(E_ n\), \(n=6,7,8\). One of the applications of these calculations gives the results of K. Mizuno [see J. Fac. Sci., Univ. Tokyo, Sect. I A 24, 525-563 (1977; Zbl 0399.20044)] on the order relation for unipotent orbits in G given by inclusion of Zariski closures.
Reviewer: A.G.Elashvili

20G40 Linear algebraic groups over finite fields
20G15 Linear algebraic groups over arbitrary fields
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