A restriction theorem and the Poincaré series for \(U\)-invariants
type: Item
instance of: scholarly article
title: A restriction theorem and the Poincaré series for \(U\)-invariants
zbMATH Open document ID: 0820.14033
DOI: 10.1007/BF01446653
author: Dmitri I. Panyushev
published in: Mathematische Annalen
publication date: 1995-09-17T00:00:00Z
full work available at URL: https://eudml.org/doc/165313
review text: Let \(X\) be a normal irreducible affine variety acted on by a connected semisimple group \(G\). We study regular functions on \(X\), which are invariant relative to a maximal unipotent subgroup \(U\) of \(G\). We prove a theorem that allows us to reduce the finding of the algebra of \(U\)- invariants to an action of a smaller group on a subvariety of \(X\). The algebra of \(U\)-invariants on \(X\) always has a natural grading and we give several inequalities for the degree of the related Poincaré series. Applications of these results to \(U\)-invariants of affine double cones and to decompositions of tensor products of irreducible representations of \(G\) are given.
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 759288
zbMATH Keywords: group action
zbMATH Keywords: invariant regular functions
zbMATH Keywords: Poincaré series
MaRDI profile type: Publication
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OpenAlex ID: W2063087022
description: scientific article; zbMATH DE number 759288