On actions of a maximal torus on orbits of highest weight vectors
type: Item
instance of: scholarly article
title: On actions of a maximal torus on orbits of highest weight vectors
zbMATH Open document ID: 0937.20023
author: Dmitri I. Panyushev
published in: Journal of Algebra
publication date: 2000-03-09T00:00:00Z
review text: Let \(G\) be a semi-simple, simply connected algebraic group defined over an algebraically closed field of characteristic 0. Let \(T\) be a maximal torus and \(B\) a Borel subgroup containing \(T\). For a dominant weight \(\lambda\), let \(V(\lambda)\) be the irreducible \(G\)-module with highest weight \(\lambda\). Let \(C(\lambda)\) denote the closure of the \(G\)-orbit of the highest weight vectors in \(V(\lambda)\). The author characterizes the \(\lambda\)'s for which the quotient map \(C(\lambda)\to C(\lambda)//T\) is equidimensional; the author also characterizes the \(\lambda\)'s for which the quotient map \(C(\lambda)//T\) is an affine space, i.e., \(k[C(\lambda)]^T\) is a polynomial algebra. The author also describes the canonical module of \(k[C(\lambda)]^T\).
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 1271827
zbMATH Keywords: equidimensional quotient maps
zbMATH Keywords: semi-simple simply connected algebraic groups
zbMATH Keywords: maximal tori
zbMATH Keywords: Borel subgroups
zbMATH Keywords: dominant weights
zbMATH Keywords: irreducible modules
zbMATH Keywords: highest weights
zbMATH Keywords: affine spaces
zbMATH Keywords: polynomial algebras
zbMATH Keywords: canonical modules
reviewed by: V. Lakshmibai
MaRDI profile type: Publication
full work available at URL: jabr.1998.7632
OpenAlex ID: W2011835004
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DOI: 10.1006/JABR.1998.7632
description: scientific article; zbMATH DE number 1271827