Vinberg's θ-groups in positive characteristic and Kostant-Weierstrass slices
Abstract
Description
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 good characteristic), confirming a conjecture of Popov in this case.
36 pages. Some proofs improved, one or two references added
36 pages. Some proofs improved, one or two references added