A Littlewood-Richardson filtration at roots of 1 for quantum deformations of skew Schur modules
type: Item
instance of: scholarly article
title: A Littlewood-Richardson filtration at roots of 1 for quantum deformations of skew Schur modules
zbMATH Open document ID: 0854.16025
author: Giandomenico Boffi
author: Michela Varagnolo
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1997-01-21T00:00:00Z
review text: It is well known that the classical skew Schur module is isomorphic to a direct sum of (non-skew) Schur modules, the multiplicities being given by the Littlewood-Richardson rule. We define a multiparameter quantum deformation of the classical skew Schur module, and show that up to a filtration, it still has a Littlewood-Richardson decomposition. The ground ring can be any commutative ring, and \(q\) is allowed to be a root of 1.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16S80
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 927282
zbMATH Keywords: skew Schur modules
zbMATH Keywords: direct sums
zbMATH Keywords: multiplicities
zbMATH Keywords: Littlewood-Richardson rule
zbMATH Keywords: multiparameter quantum deformations
zbMATH Keywords: filtrations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225383
OpenAlex ID: W1968749417
cites work: Schur functors and Schur complexes
cites work: Characteristic-free decomposition of skew Schur functors
cites work: Multiparameter quantum function algebra at roots of 1
cites work: Quantum groups and quantum determinants
cites work: Quantum multilinear algebra
cites work: Multiparameter quantum groups and twisted quasitriangular Hopf algebras
cites work: Q3209285
DOI: 10.2748/TMJ/1178225383
Recommended article: Little \(q\)-Schur algebras at even roots of unity
Recommended article: Schubert filtration and quasidifferentiation in quantum Serre algebras
Recommended article: Littlewood-Richardson coefficients for Hecke algebras at roots of unity
Recommended article: Irreducible modules of quantized enveloping algebras at roots of 1
Recommended article: Filtrations in Modular Representations of Reductive Lie Algebras
Recommended article: Irreducible modules of quantized enveloping algebras at roots of 1, ii
Recommended article: A \(q\)-deformation of Wakimoto modules, primary fields and screening operators
Recommended article: De Concini-Kac filtration and Gelfand-Tsetlin generators for quantum \(\mathfrak{gl}_N\)
Recommended article: Filtered deformations of elliptic algebras
Recommended article: Loewy filtration and quantum de Rham cohomology over quantum divided power algebra
description: scientific article; zbMATH DE number 927282