Journal of Noncommutative Geometry

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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) Laboratoire AGM et Département de Mathématiques, Université de Cergy-Pontoise, 95000, Cergy-Pontoise, France
(2) Laboratoire de Mathématiques Nicolas Oresme, Université de Caen, BP 5186, 14032, Caen CEDEX, France

We find the fusion rules for the quantum analogues of the complex reflection groups Hsn = ℤsSn. The irreducible representations can be indexed by the elements of the free monoid ℕs, 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

Banica Teodor, Vergnioux Roland: Fusion rules for quantum reflection groups. J. Noncommut. Geom. 3 (2009), 327-359. doi: 10.4171/JNCG/39