On the action of Ariki-Koike algebras on tensor space.
type: Item
instance of: scholarly article
title: On the action of Ariki-Koike algebras on tensor space.
zbMATH Open document ID: 1146.20002
author: Friederike Stoll
published in: Journal of Algebra
publication date: 2008-07-11T00:00:00Z
review text: The author introduces a new algebra \(\mathcal H\) by generators and relations which always satisfies the double centralizer property with a Levi subalgebra of some \(q\)-Schur algebra. With these new algebras, she shows that the Ariki-Koike algebra is isomorphic to a direct sum of matrix rings over some smaller Ariki-Koike algebra when the separation condition holds, which gives a refinement of the Dipper-Mathas Morita equivalence. She also compares this new algebra \(\mathcal H\) with Shoji's modified Ariki-Koike algebra and proves that they are isomorphic to each other when \(u_i-u_j\) is invertible for any \(i\neq j\).
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 16D90
zbMATH DE Number: 5300813
zbMATH Keywords: Ariki-Koike algebras
zbMATH Keywords: Schur-Weyl duality
zbMATH Keywords: \(q\)-Schur algebras
zbMATH Keywords: Levi subalgebras
zbMATH Keywords: Shoji algebras
zbMATH Keywords: double centralizer property
zbMATH Keywords: tensor spaces
zbMATH Keywords: endomorphism algebras
zbMATH Keywords: quantum groups
zbMATH Keywords: Hecke algebras
reviewed by: Hu Jun
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2007.10.008
OpenAlex ID: W2123498496
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DOI: 10.1016/J.JALGEBRA.2007.10.008
description: scientific article; zbMATH DE number 5300813