The blocks of the \(q\)-Schur algebra
type: Item
instance of: scholarly article
title: The blocks of the \(q\)-Schur algebra
zbMATH Open document ID: 0911.16021
author: Anton Cox
published in: Journal of Algebra
publication date: 1999-03-08T00:00:00Z
review text: Results which give a partial determination of the blocks of the \(q\)-Schur algebra at roots of unity have previously been obtained by the author (for \(n=2\)), by James and Mathas (for \(n\geq d\)) and by Thams. The main result of this paper is to determine such blocks completely from the blocks of a suitable quantum general linear group, thus generalizing a result of Donkin on classical Schur algebras. The methods used involve playing the Dipper-Donkin quantization against the Manin quantization, and finding a suitable generalization of Andersen's strong linkage principle. This allows Donkins' original argument to be lifted to the quantum case. Note that \(\inf_K^H(V)\) in the statement of Proposition 4.5 should read \(\text{ind}_K^H(V)\).
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1213859
zbMATH Keywords: \(q\)-Schur algebras
zbMATH Keywords: quantum general linear groups
zbMATH Keywords: Dipper-Donkin quantization
zbMATH Keywords: Manin quantization
zbMATH Keywords: strong linkage principle
reviewed by: R. M. Green
MaRDI profile type: Publication
full work available at URL: jabr.1998.7442
OpenAlex ID: W2087051449
DOI: 10.1006/JABR.1998.7442
description: scientific article; zbMATH DE number 1213859