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, F-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