Cores of Ariki-Koike algebras

TL;DR

This paper explores the combinatorial structure of (e, s)-cores related to l-partitions and their applications in the block theory of Ariki-Koike algebras, advancing understanding of their algebraic properties.

Contribution

It introduces the concept of (e, s)-cores for l-partitions and connects them to the block theory of Ariki-Koike algebras, extending previous combinatorial frameworks.

Findings

Characterization of (e, s)-cores for l-partitions

Application of (e, s)-cores to block classification in Ariki-Koike algebras

Enhanced understanding of the combinatorial and algebraic interplay

Abstract

We study a natural generalization of the notion of cores for l-partitions attached with a multi-charge s $\in$ Z^l : the (e, 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.