On the regularization process for Ariki-Koike algebras

TL;DR

This paper extends theorems related to modular representations from symmetric groups to complex reflection groups of type G(l,1,n) and their Ariki-Koike algebras, broadening understanding of their algebraic structures.

Contribution

It generalizes existing theorems on modular representations to Ariki-Koike algebras associated with complex reflection groups G(l,1,n).

Findings

Extended theorems to a broader class of algebras.

Provided new insights into the structure of Ariki-Koike algebras.

Enhanced understanding of modular representation theory for complex reflection groups.

Abstract

The aim of this note is to study a generalization of theorems by James and Fayers on the modular representations of the symmetric group and its Hecke algebra to the case of the complex reflection groups of type $G(l,1,n)$ and the associated Ariki-Koike algebra.