Rouquier blocks of the cyclotomic Hecke algebras of G(de,e,r)

TL;DR

This paper determines Rouquier blocks for cyclotomic Hecke algebras of the infinite series G(de,e,r), extending the understanding of their structure across all complex reflection groups.

Contribution

It completes the calculation of Rouquier blocks for all complex reflection groups, specifically for the G(de,e,r) series.

Findings

Rouquier blocks are explicitly determined for G(de,e,r)

The results extend the applicability of Rouquier blocks to all complex reflection groups

Provides a comprehensive classification of blocks for these algebras

Abstract

The "Rouquier blocks" of the cyclotomic Hecke algebras, introduced by Rouquier, are a substitute for the "families of characters", defined by Lusztig for Weyl groups, which can be applied to all complex reflection groups. In this article, we determine them for the cyclotomic Hecke algebras of the groups of the infinite series, G(de,e,r), thus completing their calculation for all complex reflection groups.