The semisimple conjugacy classes and the generic class number of the finite simple groups of Lie type \(E_ 8\). (English) Zbl 0816.20015
Let \(G\) be a simple, algebraic group of exceptional type \(E_ 8\) over an algebraically closed field \(K\) of characteristic \(p > 0\) and defined over the finite field \(\mathbb{F}_ q\), where \(q\) is a power of \(p\). Let \(F\) be the corresponding Frobenius morphism of \(G\), and \(G^ F\) the fixed point group, which is the finite simple group of Lie type \(E_ 8\). The authors determine the semisimple conjugacy classes of \(G^ F\) as well as the total number of conjugacy classes, given as a polynomial in \(q\).
The corresponding results for adjoint groups of type \(E_ 6\) and \(E_ 7\) can be found in the authors’ paper [Commun. Algebra 21, 93-161 (1993; Zbl 0813.20015)].
The corresponding results for adjoint groups of type \(E_ 6\) and \(E_ 7\) can be found in the authors’ paper [Commun. Algebra 21, 93-161 (1993; Zbl 0813.20015)].
Reviewer: Ye Jiachen (Shanghai)
MSC:
20C33 | Representations of finite groups of Lie type |
20D06 | Simple groups: alternating groups and groups of Lie type |
20G40 | Linear algebraic groups over finite fields |
20G05 | Representation theory for linear algebraic groups |
Keywords:
algebraic group; finite simple group of Lie type \(E_ 8\); semisimple conjugacy classes; adjoint groupsCitations:
Zbl 0813.20015References:
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[3] | DOI: 10.1080/00927879208824553 · Zbl 0813.20015 · doi:10.1080/00927879208824553 |
[4] | Mizuno K., J. Fac. Sci. Univ. Tokyo 24 pp 525– (1977) |
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