Modular Littlewood-Richardson coefficients
type: Item
instance of: scholarly article
title: Modular Littlewood-Richardson coefficients
zbMATH Open document ID: 0945.20027
author: Jonathan Brundan
author: Alexander S. Kleshchev
published in: Mathematische Zeitschrift
publication date: 2000-02-01T00:00:00Z
review text: The authors study the polynomial representations of the general linear group \(\text{GL}_n(F)\) and modular representations of the symmetric group \(\Sigma_r\) over \(F\), where \(F\) is an algebraically closed field of characteristic \(p>0\). If \(p=0\), then the classical Littlewood-Richardson coefficients describe the decomposition of all the following modules: (M1) the restriction of an irreducible \(\text{GL}_n(F)\)-module to a Levi subgroup of \(\text{GL}_n(F)\); (M2) the tensor product of irreducible \(\text{GL}_n(F)\)-modules; (M3) the restriction of an irreducible \(\Sigma_r\)-module to a Young subgroup of \(\Sigma_r\); (M4) the \(\Sigma_r\)-module induced from an irreducible module for a Young subgroup. In the modular case, one has tilting modules (for the general linear group) and Young modules (for the symmetric group). The goal of this paper is to deal with the case of positive characteristic. The authors describe three quite different sources of connections between them, and obtain connections between various `modular Littlewood-Richardson coefficients'. In particular, they compute certain modular Littlewood-Richardson coefficients exactly.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 1384390
zbMATH Keywords: general linear groups
zbMATH Keywords: polynomial representations
zbMATH Keywords: symmetric groups
zbMATH Keywords: modular representations
zbMATH Keywords: Littlewood-Richardson coefficients
zbMATH Keywords: irreducible modules
zbMATH Keywords: Young subgroups
zbMATH Keywords: tilting modules
MaRDI profile type: Publication
full work available at URL: s002090050516
OpenAlex ID: W1965769910
DOI: 10.1007/S002090050516
description: scientific article; zbMATH DE number 1384390