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A simple proof of Pommerening's theorem
- Source :
-
Journal of Algebra . Sep2008, Vol. 320 Issue 5, p2196-2208. 13p. - Publication Year :
- 2008
-
Abstract
- Abstract: Let G be a connected reductive algebraic group over an algebraically closed field of characteristic . Assume that p is good for G. Pommerening''s theorem [K. Pommerening, Über die unipotenten Klassen reduktiver Gruppen, J. Algebra 49 (1977) 525–536; K. Pommerening, Über die unipotenten Klassen reduktiver Gruppen, II, J. Algebra 65 (1980) 373–398] asserts that any distinguished nilpotent element in the Lie algebra of G is a Richardson element for a distinguished parabolic subgroup of G. This theorem implies the Bala–Carter theorem in good characteristic. In this paper we give a short proof of Pommerening''s theorem, which is a further simplification of Premet''s first uniform proof [A. Premet, Nilpotent orbits in good characteristic and the Kempf–Rousseau theory, J. Algebra 260 (2003) 338–366]. We also simplify Premet''s proof of the existence theorem for good transverse slices to the nilpotent -orbits in . [Copyright &y& Elsevier]
- Subjects :
- *MATHEMATICAL analysis
*MATHEMATICS
*DIFFERENTIAL equations
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 320
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 33467389
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2008.04.028