KW-sections for exceptional type Vinberg's $\theta$-groups
Rings and Algebras
2010-05-12 v2 Group Theory
Abstract
Let be an algebraically closed field of characteristic not equal to 2 or 3, let be an almost simple algebraic group of type , or and let be an automorphism of of finite order, coprime to the characteristic. In this paper we consider the -group (in the sense of Vinberg) associated to these choices; we classify the positive rank automorphisms and give their Kac diagrams and we describe the little Weyl group in each case. As a result we show that all such -groups have KW-sections, confirming a conjecture of Popov in these cases.
Cite
@article{arxiv.0805.2064,
title = {KW-sections for exceptional type Vinberg's $\theta$-groups},
author = {Paul Levy},
journal= {arXiv preprint arXiv:0805.2064},
year = {2010}
}
Comments
Fairly substantially revised, correction to table 2 (including the automorphism with diagram 01001) and to the relevant sections of the text. 25 pages, 3 tables.