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    Rights statement: The final, definitive version of this article has been published in the Journal, Journal of Algebra 389, 2013, © ELSEVIER.

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

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>1/09/2013
<mark>Journal</mark>Journal of Algebra
Volume389
Number of pages20
Pages (from-to)78-97
Publication statusPublished
Original languageEnglish

Abstract

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.

Bibliographic note

The final, definitive version of this article has been published in the Journal, Journal of Algebra 389, 2013, © ELSEVIER.