Resumen de Representations of Ariki- Koike algebras and Gröbner- Shirshov bases

Seok-Jin Kang, In-Sok Lee, Kyu-Hwan Lee, Hyekyung Oh

• 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 $\lambda$.