Rouquier blocks of the cyclotomic Ariki-Koike algebras

TL;DR

This paper introduces an algorithm to determine Rouquier blocks in cyclotomic Ariki-Koike algebras, extending the concept from Weyl groups to complex reflection groups, aiding in understanding their representation theory.

Contribution

It provides the first explicit algorithm for identifying Rouquier blocks in cyclotomic Ariki-Koike algebras, generalizing previous notions from Weyl groups.

Findings

Algorithm successfully determines Rouquier blocks

Extends Rouquier's concept to complex reflection groups

Facilitates further research in algebraic representation theory

Abstract

The definition of Rouquier for the families of characters of Weyl groups in terms of blocks of the associated Iwahori-Hecke algebra has made possible the generalization of this notion to the complex reflection groups. Here we give an algorithm for the determination of the "Rouquier blocks" of the cyclotomic Ariki-Koike algebras.