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- W126373124 abstract "In this paper, we find the fusion rules for the free wreath product quantum groups $mathbb{G}wr_*S_N^+$ for all compact matrix quantum groups of Kac type $mathbb{G}$ and $Nge4$. This is based on a combinatorial description of the intertwiner spaces between certain generating representations of $mathbb{G}wr_*S_N^+$. The combinatorial properties of the intertwiner spaces in $mathbb{G}wr_*S_N^+$ then allows us to obtain several probabilistic applications. We then prove the monoidal equivalence between $mathbb{G}wr_*S_N^+$ and a compact quantum group whose dual is a discrete quantum subgroup of the free product $widehat{mathbb{G}}*widehat{SU_q(2)}$, for some $0<qle1$. We obtain as a corollary certain stability results for the operator algebras associated with the free wreath products of quantum groups such as Haagerup property, weak amenability and exactness." @default.
- W126373124 created "2016-06-24" @default.
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- W126373124 date "2014-11-15" @default.
- W126373124 modified "2023-09-27" @default.
- W126373124 title "Free wreath product quantum groups : the monoidal category, approximation properties and free probability" @default.
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