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

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.

In the second version, we study a missing (from the first version) case in the proof of Theorem 3.10 (without consequences on the result). Moreover, Lemma 4.7 is added in order to obtain the proof of the result stated in Theorem 4.8