Fusion rules for quantum reflection groups

Abstract

We find the fusion rules for the quantum analogues of the complex reflection groups $H_n^s=Z_s\wr S_n$. The irreducible representations can be indexed by the elements of the free monoid $N^{\ast s}$, and their tensor products are given by formulae which remind the Clebsch–Gordan rules (which appear at $s=1$).