Publications
Detailed Information
Representations of Ariki-Koike algebras and Grobner-Shirshov bases
Cited 0 time in
Web of Science
Cited 0 time in Scopus
- Authors
- Issue Date
- 2004-07
- Publisher
- Oxford University Press
- Citation
- Proc. London Math. Soc.(3) 89 (2004) 54-70
- Keywords
- Ariki–Koike algebras ; Specht modules ; Gröbner–Shirshov basis ; tableaux
- 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
- Files in This Item:
- There are no files associated with this item.
- Appears in Collections:
Item View & Download Count
Items in S-Space are protected by copyright, with all rights reserved, unless otherwise indicated.