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Fusion rules for quantum reflection groups. (English) Zbl 1203.46048

The paper under review is concerned with the investigation of \(H_n^{s+}\) – a quantum version of the classical group of \(n\) by \(n\) monomial unitary matrices whose nonzero entries are \(s\)-th roots of unity. The authors show that \(H_n^{s+}\) is a free wreath product of the cyclic group \(\mathbb{Z}_s\) with the quantum permutation group \(S^+_n\), describe the corepresentation theory of \(H_n^{s+}\) in terms of a certain category of non-crossing partitions, and identify explicitly the resulting fusion ring (in particular, computing the dimensions of irreducible unitary corepresentations).

MSC:

46L65 Quantizations, deformations for selfadjoint operator algebras
16T20 Ring-theoretic aspects of quantum groups
17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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