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Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices

Research output: Contribution to journalJournal article

Published

Journal publication date06/2009
JournalTransformation Groups
Journal number2
Volume14
Number of pages45
Pages417-461
Original languageEnglish

Abstract

We generalize the basic results of Vinberg’s θ-groups, or periodically graded reductive Lie algebras, to fields of good positive characteristic. To this end we clarify the relationship between the little Weyl group and the (standard) Weyl group. We deduce that the ring of invariants associated to the grading is a polynomial ring. This approach allows us to prove the existence of a KW-section for a classical graded Lie algebra (in zero or odd positive characteristic), confirming a conjecture of Popov in this case.