Relative equidimensionality and stability of actions of a reductive algebraic group
type: Item
instance of: scholarly article
title: Relative equidimensionality and stability of actions of a reductive algebraic group
zbMATH Open document ID: 0965.20028
author: Haruhisa Nakajima
published in: Manuscripta Mathematica
publication date: 2001-05-09T00:00:00Z
review text: The author introduces and studies relative versions of equidimensionality and stability, notions of algebraic transformation groups theory. They are called relative quasi-equidimensionality and relative stability of actions of affine algebraic groups, especially of reductive groups, on affine varieties. As an application, for complex reductive groups of semisimple rank one, the author characterizes relatively stable representations and relatively equidimensional representations, and shows that every equidimensional representation is cofree.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 13A50
zbMATH DE Number: 1491671
zbMATH Keywords: affine algebraic groups
zbMATH Keywords: actions
zbMATH Keywords: affine varieties
zbMATH Keywords: quotient maps
zbMATH Keywords: representations
zbMATH Keywords: polynomial invariants
zbMATH Keywords: equidimensionality
zbMATH Keywords: stability
zbMATH Keywords: reductive groups
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
full work available at URL: s002291020139
OpenAlex ID: W1975192013
DOI: 10.1007/S002291020139
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description: scientific article; zbMATH DE number 1491671