Fusion rules for quantum reflection groups

Abstract

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