Nilpotent orbits in good characteristic and the Kempf–Rousseau theory
✍ Scribed by Alexander Premet
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 318 KB
- Volume
- 260
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic p > 0, g = Lie G, and suppose that p is a good prime for the root system of G. In this paper, we give a fairly short conceptual proof of Pommerening's theorem [Pommerening, J. Algebra 49 (1977) 525-536; J. Algebra 65 (1980) 373-398] which states that any nilpotent element in g is Richardson in a distinguished parabolic subalgebra of the Lie algebra of a Levi subgroup of G. As a by-product, we obtain a short noncomputational proof of the existence theorem for good transverse slices to the nilpotent G-orbits in g (for earlier proofs of this theorem see [