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Representations of Ariki-Koike algebras and Grobner-Shirshov bases

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Authors
Kang, Seok-Jin; Lee, In-Sok; Lee, Kyu-Hwan; Oh, Hyekyung
Issue Date
2004-07
Publisher
Oxford University Press
Citation
Proc. London Math. Soc.(3) 89 (2004) 54-70
Keywords
Ariki–Koike algebrasSpecht modulesGröbner–Shirshov basistableaux
Abstract
In this paper, we investigate the structure of Ariki–Koike algebras and their Specht modules using Gröbner–Shirshov basis theory and combinatorics of Young tableaux. For a multipartition $\lambda$, we find a presentation of the Specht module $S^{\lambda}$ given by generators and relations, and determine its Gröbner–Shirshov pair. As a consequence, we obtain a linear basis of $S^{\lambda}$ consisting of standard monomials with respect to the Gröbner–Shirshov pair. We show that this monomial basis can be canonically identified with the set of cozy tableaux of shape $\lambda$.
ISSN
0024-6115
Language
English
URI
http://hdl.handle.net/10371/12154
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)