On the representation theory of partition (easy) quantum groups - Archive ouverte HAL
Article Dans Une Revue Journal für die reine und angewandte Mathematik Année : 2016

On the representation theory of partition (easy) quantum groups

Résumé

Compact matrix quantum groups are strongly determined by their intertwiner spaces, due to a result by S. L. Woronowicz. In the case of easy quantum groups (also called partition quantum groups), the intertwiner spaces are given by the combinatorics of partitions, see the initial work of T. Banica and R. Speicher. The philosophy is that all quantum algebraic properties of these objects should be visible in their combinatorial data. We show that this is the case for their fusion rules (i.e. for their representation theory). As a byproduct, we obtain a unified approach to the fusion rules of the quantum permutation group SC N, the free orthogonal quantum group OC N as well as the hyperoctahedral quantum group H C N . We then extend our work to unitary easy quantum groups and link it with a “freeness conjecture” of T. Banica and R. Vergnioux.
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Dates et versions

hal-03817237 , version 1 (08-05-2024)

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Citer

Amaury Freslon, Moritz Weber. On the representation theory of partition (easy) quantum groups. Journal für die reine und angewandte Mathematik, 2016, 2016 (720), pp.155-197. ⟨10.1515/crelle-2014-0049⟩. ⟨hal-03817237⟩
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