Levy, Paul (2009) Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices. Transformation Groups, 14 (2). pp. 417-461. ISSN 1531-586XFull text not available from this repository.
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.
|Journal or Publication Title:||Transformation Groups|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||09 Dec 2011 13:34|
|Last Modified:||09 Apr 2014 22:56|
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