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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

##### MSC:
 20G40 Linear algebraic groups over finite fields 20G15 Linear algebraic groups over arbitrary fields
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##### References:
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