Blocks of Ariki-Koike algebras and level-rank duality

TL;DR

This paper explores the structure of blocks in Ariki-Koike algebras through a generalized core concept for l-partitions, linking affine symmetric group actions to level-rank duality and analyzing their orbits.

Contribution

It introduces a new approach to understanding blocks in Ariki-Koike algebras via a generalized core for l-partitions and connects affine symmetric group actions to level-rank duality.

Findings

Characterization of blocks using generalized cores

Interpretation of affine symmetric group actions in level-rank duality

Analysis of orbits under group actions

Abstract

We study the blocks for Ariki-Koike algebras using a general notion of core for $l$-partitions. We interpret the action of the affine symmetric group on the blocks in the context of level rank duality and study the orbits under this action.