On double centralizer properties between quantum groups and Ariki-Koike algebras.
type: Item
instance of: scholarly article
title: On double centralizer properties between quantum groups and Ariki-Koike algebras.
zbMATH Open document ID: 1092.20006
author: Hu Jun
author: Friederike Stoll
published in: Journal of Algebra
publication date: 2004-10-04T00:00:00Z
review text: The authors study the double centralizer properties for tensor spaces as bimodules over quantum groups and Ariki-Koike algebras [\textit{S. Ariki} and \textit{K. Koike}, Adv. Math. 106, No. 2, 216-243 (1994; Zbl 0840.20007)] and their relations with \textit{T. Shoji}'s algebras \(H^h\) [J. Algebra 226, No. 2, 818-856 (2000; Zbl 0959.20007)]. It is proved that, under the separation condition, [\textit{S. Ariki}, J. Reine Angew. Math. 513, 53-69 (1999; Zbl 0972.17011)], the natural homomorphism from the Ariki-Koike algebra to the endomorphism algebra of tensor space as module over quantum group is surjective. It is also proved that the natural homomorphism from Shoji's algebra \(H^h\) to the endomorphism algebra is always surjective, and \(H^h\) is actually isomorphic to a direct sum of matrix algebras over some Hecke algebras of type \(A\).
reviewed by: Ahmed A. Khammash
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16S50
zbMATH DE Number: 2105801
zbMATH Keywords: Shoji algebras
zbMATH Keywords: Ariki-Koike algebras
zbMATH Keywords: double centralizer property
zbMATH Keywords: tensor spaces
zbMATH Keywords: endomorphism algebras
zbMATH Keywords: quantum groups
zbMATH Keywords: Hecke algebras
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2003.10.026
OpenAlex ID: W1976388168
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DOI: 10.1016/J.JALGEBRA.2003.10.026
description: scientific article; zbMATH DE number 2105801