Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices
AU - Levy, Paul
PY - 2009/6
Y1 - 2009/6
N2 - 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.
AB - 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.
U2 - 10.1007/s00031-009-9056-y
DO - 10.1007/s00031-009-9056-y
M3 - Journal article
VL - 14
SP - 417
EP - 461
JO - Transformation Groups
JF - Transformation Groups
SN - 1531-586X
IS - 2
ER -