Vinberg's theta-groups in positive characteristic and Kostant-Weierstrass slices

We generalize the basic results of Vinberg's theta-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.


Published in:
Transformation Groups, 14, 417-461
Year:
2009
Publisher:
Springer Verlag
ISSN:
1083-4362
Keywords:
Laboratories:




 Record created 2010-11-30, last modified 2018-03-17


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