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

Levy, Paul (2009) Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices. Transformation Groups, 14 (2). pp. 417-461.

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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.

Item Type:	Article
Journal or Publication Title:	Transformation Groups
Subjects:	UNSPECIFIED
Departments:	Faculty of Science and Technology > Mathematics and Statistics
ID Code:	51959
Deposited By:	ep_importer_pure
Deposited On:	09 Dec 2011 13:34
Refereed?:	Yes
Published?:	Published
Last Modified:	26 Jul 2012 19:59
Identification Number:
URI:	http://eprints.lancs.ac.uk/id/eprint/51959

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