A new stability property of plethysm
type: Item
instance of: scholarly article
title: A new stability property of plethysm
zbMATH Open document ID: 0876.20025
DOI: 10.1007/BF02566432
author: Pierre-Louis Montagard
published in: Commentarii Mathematici Helvetici
publication date: 1996-12-17T00:00:00Z
full work available at URL: https://eudml.org/doc/140410
review text: Let \(G\) be a connected reductive algebraic group over \(\mathbb{C}\). Let \(\lambda\), \(\mu\), \(\nu\) be its dominant weights, \(\pi\), \(\theta\) partitions of an integer \(p\) and \(V_\nu\) a simple \(G\)-module with the highest weight \(\nu\). The author investigates the behaviour of the multiplicity of a simple \(G\)-module with the highest weight \(\mu+n\lambda\) in \(S_{\pi+n\theta}V_\nu\) when \(n\) tends to infinity. It is shown that this multiplicity always increases but not always becomes stable. A combinatorial criterion of stability is given. The principal result gives some necessary conditions for appearance of an irreducible representation in the plethysm.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20G20
zbMATH DE Number: 949856
zbMATH Keywords: irreducible representations
zbMATH Keywords: plethysm
zbMATH Keywords: connected reductive algebraic groups
zbMATH Keywords: dominant weights
zbMATH Keywords: highest weights
zbMATH Keywords: multiplicity of simple modules
zbMATH Keywords: stability
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 949856