Weights of multipartitions and representations of Ariki-Koike algebras. II: Canonical bases
type: Item
instance of: scholarly article
title: Weights of multipartitions and representations of Ariki-Koike algebras. II: Canonical bases
zbMATH Open document ID: 1201.17006
author: Matthew Fayers
published in: Journal of Algebra
publication date: 2008-05-21T00:00:00Z
review text: The author continues his study of Ariki-Koike algebras (cyclotomic Hecke algebras) begun in [Adv. Math. 206, No. 1, 112--144 (2006; Zbl 1111.20009)] where he introduced a notion of `weight' for multipartitions. Here he considers the canonical basis for an integrable highest-weight module of the quantum algebra \(U_v(\widehat{\mathfrak{sl}}_e)\) and shows how the relationship between different canonical bases is controlled by the weight of a multipartition, generalizing a theorem of \textit{A. Lascoux, B. Leclerc} and \textit{J.-Y. Thibon} [Commun. Math. Phys. 181, 205--263 (1996; Zbl 0874.17009)] for the level 1 case.
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 5277622
zbMATH Keywords: multipartitions
zbMATH Keywords: Ariki-Koike algebras
zbMATH Keywords: canonical bases
zbMATH Keywords: weight
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2007.10.002
OpenAlex ID: W1964165002
cites work: On the decomposition numbers of the Hecke algebra of \(G(m,1,n)\)
cites work: On the classification of simple modules for cyclotomic Hecke algebras of type \(G(m,1,n)\) and Kleshchev multipartitions
cites work: Proof of the modular branching rule for cyclotomic Hecke algebras.
cites work: A Hecke algebra of \((\mathbb{Z}/r\mathbb{Z})\wr{\mathfrak S}_ n\) and construction of its irreducible representations
cites work: The number of simple modules of the Hecke algebras of type \(G(r,1,n)\)
cites work: Q4279641
cites work: Q4426036
cites work: Morita equivalences of Ariki-Koike algebras.
cites work: Weights of multipartitions and representations of Ariki-Koike algebras.
cites work: Core blocks of Ariki-Koike algebras.
cites work: Q4248254
cites work: Cellular algebras
cites work: Q4317267
cites work: Strong multiplicity one theorems for affine Hecke algebras of type \(A\).
cites work: Q-analogues of Clifford and Weyl algebras - spinor and oscillator representations of quantum enveloping algebras
cites work: Q4435149
cites work: Hecke algebras at roots of unity and crystal bases of quantum affine algebras
cites work: Blocks of cyclotomic Hecke algebras.
cites work: Q4699474
cites work: Tilting modules for cyclotomic Schur algebras
cites work: Crystal base for the basic representation of \(U_ q({\mathfrak sl}^\wedge (n))\)
cites work: Bijections of p -Regular Partitions and p -Modular Irreducibles of the Symmetric Groups
DOI: 10.1016/J.JALGEBRA.2007.10.002
description: scientific article; zbMATH DE number 5277622