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

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Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices. / Levy, Paul.
In: Transformation Groups, Vol. 14, No. 2, 06.2009, p. 417-461.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Levy, P 2009, 'Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices', Transformation Groups, vol. 14, no. 2, pp. 417-461. https://doi.org/10.1007/s00031-009-9056-y

APA

Levy, P. (2009). Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices. Transformation Groups, 14(2), 417-461. https://doi.org/10.1007/s00031-009-9056-y

Vancouver

Levy P. Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices. Transformation Groups. 2009 Jun;14(2):417-461. doi: 10.1007/s00031-009-9056-y

Author

Levy, Paul. / Vinberg’s θ-groups in positive characteristic and Kostant–Weierstrass slices. In: Transformation Groups. 2009 ; Vol. 14, No. 2. pp. 417-461.

Bibtex

@article{6ebadb6fb657435dab2ca5757c092659,
title = "Vinberg{\textquoteright}s θ-groups in positive characteristic and Kostant–Weierstrass slices",
abstract = "We generalize the basic results of Vinberg{\textquoteright}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.",
author = "Paul Levy",
year = "2009",
month = jun,
doi = "10.1007/s00031-009-9056-y",
language = "English",
volume = "14",
pages = "417--461",
journal = "Transformation Groups",
issn = "1531-586X",
publisher = "Birkhause Boston",
number = "2",

}

RIS

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 -