A geometrical approach to the Littlewood-Richardson rule
type: Item
instance of: scholarly article
title: A geometrical approach to the Littlewood-Richardson rule
zbMATH Open document ID: 0882.20027
author: Bhama Srinivasan
published in: Journal of Algebra
publication date: 1998-03-09T00:00:00Z
review text: Let \(L\) be a subgroup of \(G=\text{GL}(n,C)\) isomorphic to \(\text{GL}(m,C)\times\text{GL}(n-m,C)\), \(W\) the Weyl group of \(G\) and \(W'\) the Weyl group of \(L\). The Littlewood-Richardson rule gives the decomposition of an induced representation of an irreducible representation of \(W'\) into irreducible representations of \(W\). The author describes the right cells of \(W\) which arise in the induced representation of a right cell of \(W'\), by means of the corresponding standard tableaux. Then given a pair of standard tableaux corresponding to an irreducible representation of \(W'\), she attaches to them a set of standard tableaux corresponding to the irreducible constituents of the induced representation of \(W\). This can be regarded as a reformulation and a refinement of the Littlewood-Richardson rule.
reviewed by: Chiu Sen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 1014040
zbMATH Keywords: Weyl groups
zbMATH Keywords: Littlewood-Richardson rule
zbMATH Keywords: induced representations
zbMATH Keywords: irreducible representations
zbMATH Keywords: right cells
zbMATH Keywords: standard tableaux
MaRDI profile type: Publication
full work available at URL: jabr.1997.6784
OpenAlex ID: W2087069427
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DOI: 10.1006/JABR.1997.6784
description: scientific article; zbMATH DE number 1014040