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Factorization of the canonical bases for higher-level Fock spaces

Part of: Representation theory of groups Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  20 June 2011

Susumu Ariki ,
Nicolas Jacon  and
Cédric Lecouvey
Susumu Ariki
Affiliation:
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka 560-0043, Japan
Nicolas Jacon
Affiliation:
UFR Sciences et Techniques, 16 Route de Gray, 25030 Besançon, France ([email protected])
Cédric Lecouvey
Affiliation:
Faculté des Sciences et Techniques, Université François Rabelais, Parc de Grandmont, 37200 Tours, France
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Abstract

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The level l Fock space admits canonical bases and . They correspond to and -module structures. We establish that the transition matrices relating these two bases are unitriangular with coefficients in ℕ[v]. Restriction to the highest-weight modules generated by the empty l-partition then gives a natural quantization of a theorem by Geck and Rouquier on the factorization of decomposition matrices which are associated to Ariki–Koike algebras.

Keywords

Kashiwara–Lusztig canonical basisFock spacedecomposition matricescyclotomic Hecke algebras

MSC classification

Secondary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations 20C08: Hecke algebras and their representations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 55 , Issue 1 , February 2012 , pp. 23 - 51
Copyright
Copyright © Edinburgh Mathematical Society 2011

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