The Calogero-Moser partition for G(m,d,n)

Abstract

We show that it is possible to deduce the Calogero-Moser partition of the irreducible representations of the complex reflection groups $G(m,d,n)$ from the corresponding partition for $G(m,1,n)$. This confirms, in the case $W=G(m,d,n)$, a conjecture of Gordon and Martino relating the Calogero-Moser partition to Rouquier families for the corresponding cyclotomic Hecke algebra.