On covariants of reductive algebraic groups.
type: Item
instance of: scholarly article
title: On covariants of reductive algebraic groups.
zbMATH Open document ID: 1040.20037
DOI: 10.1016/S0019-3577(02)90010-8
author: Dmitri I. Panyushev
published in: Indagationes Mathematicae. New Series
publication date: 2002-01-01T00:00:00Z
review text: Let \(G\) be a reductive algebraic group over an algebraically closed field of characteristic zero. Assume \(G\) acts on an affine variety \(X\). Let \(x\in X\) be a point whose orbit closure \(Y=\overline{G\cdot x}\) is normal. Assume the orbit \(G\cdot x\) has a complement of codimension at least two in \(Y\). Let \(M\) be a finite dimensional \(G\)-module. Let \(M^{G_x}\) be the submodule of invariants under the stabiliser group \(G_x\). There is an evaluation map \(\varepsilon_x\) which associates to any \(G\)-equivariant polynomial morphism \(\phi: X\to M\) its value \(\phi(x)\) in \(M^{G_x}\). The main result is that \(\varepsilon_x\) is onto. Several applications are given.
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 13A50
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 1893634
zbMATH Keywords: covariants
zbMATH Keywords: multiplicity free representations
zbMATH Keywords: reductive algebraic groups
zbMATH Keywords: actions on affine varieties
reviewed by: Wilberd van der Kallen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1893634