Cores of Ariki-Koike algebras

Abstract

We study a natural generalization of the notion of cores for $l$-partitions attached with a multicharge $\mathbf{s}\in {\mathbb{Z}}^l$: the $(e,\mathbf{s})$-cores. We rely them both to the combinatorics and the notion of weight defined by Fayers. Next we study applications in the context of the block theory for Ariki-Koike algebras.