Journal of Noncommutative Geometry

Full-Text PDF (241 KB) |

Table of Contents |

JNCG summary

Volume 3, Issue 3, 2009, pp. 327–359

DOI: 10.4171/JNCG/39

Fusion rules for quantum reflection groups

Teodor Banica (1) and Roland Vergnioux (2)

(1) Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, F-31062, TOULOUSE CEDEX 9, FRANCE
(2) Laboratoire de Mathématiques Nicolas Oresme, Université de Caen, BP 5186, F-14032, CAEN CEDEX, FRANCE

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).

Keywords: Reflection group, quantum group, fusion rules