A simple proof of Pommerening's theorem.
type: Item
instance of: scholarly article
title: A simple proof of Pommerening's theorem.
zbMATH Open document ID: 1157.20024
author: Takehisa Tsujii
published in: Journal of Algebra
publication date: 2008-10-22T00:00:00Z
review text: Let \(G\) be a connected reductive algebraic group over an algebraically closed field of good characteristic \(p>0\). Pommerening's theorem asserts that any `distinguished' nilpotent element in the Lie algebra \(\mathfrak g\) of \(G\) is a Richardson element for a `distinguished' parabolic subgroup of \(G\). The aim of this paper is to give a unified proof that further simplifies the uniform proof of \textit{A. Premet} [J. Algebra 260, No. 1, 338-366 (2003; Zbl 1020.20031)]. The proof still uses Kempf-Rousseau theory but it avoids Bala-Carter theory as well as consideration of finite reductive groups. In good characteristic Bala-Carter theory is implied by Pommerening's theorem. The author also simplifies Premet's proof of the existence of good transverse slices to the nilpotent \(\text{Ad}(G)\) orbits in \(\mathfrak g\).
reviewed by: Wilberd van der Kallen
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 17B45
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 5355736
zbMATH Keywords: algebraic groups
zbMATH Keywords: Lie algebras
zbMATH Keywords: nilpotent elements
zbMATH Keywords: Bala-Carter theorem
zbMATH Keywords: Pommerening theorem
zbMATH Keywords: Kempf-Rousseau theory
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.04.028
OpenAlex ID: W2071026422
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DOI: 10.1016/J.JALGEBRA.2008.04.028
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description: scientific article; zbMATH DE number 5355736