KW-sections for Vinberg's θ-groups of exceptional type

Levy, Paul (2013) KW-sections for Vinberg's θ-groups of exceptional type. Journal of Algebra, 389. pp. 78-97. ISSN 0021-8693

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Let k be an algebraically closed field of characteristic not equal to 2 or 3, let G be an almost simple algebraic group of type F4, G2 or D4 and let \theta be an automorphism of G of finite order, coprime to the characteristic. In this paper we consider the \theta-group (in the sense of Vinberg) associated to these choices; we classify the positive rank automorphisms via Kac diagrams and we describe the little Weyl group in each case. As a result we show that all -groups in types G2, F4 and D4 have KW-sections, confirming a conjecture of Popov in these cases.

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Journal Article
Journal or Publication Title:
Journal of Algebra
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The final, definitive version of this article has been published in the Journal, Journal of Algebra 389, 2013, © ELSEVIER.
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Deposited On:
15 Sep 2014 09:11
Last Modified:
25 Sep 2022 00:47