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Representations of Ariki–Koike Algebras and Gröbner–Shirshov Bases
Author(s) -
Kang SeokJin,
Lee InSok,
Lee KyuHwan,
Oh Hyekyung
Publication year - 2004
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611503014606
Subject(s) - monomial , mathematics , basis (linear algebra) , monomial basis , young tableau , set (abstract data type) , algebra over a field , presentation (obstetrics) , pure mathematics , combinatorics , computer science , geometry , medicine , programming language , radiology
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 λ, we find a presentation of the Specht module S λ given by generators and relations, and determine its Gröbner–Shirshov pair. As a consequence, we obtain a linear basis of S λ 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 λ. 2000 Mathematics Subject Classification 16Gxx, 05Exx.