Probabilistic boundaries of finite extensions of quantum groups

Sara Malacarne; Sergey Neshveyev

doi:10.1142/s0219025717500266

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arXiv · 1704.04717

Probabilistic boundaries of finite extensions of quantum groups

Sara Malacarne·Sergey Neshveyev

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Abstract

Given a discrete quantum group $H$ with a finite normal quantum subgroup $G$, we show that any positive, possibly unbounded, harmonic function on $H$ with respect to an irreducible invariant random walk is $G$-invariant. This implies that, under suitable assumptions, the Poisson and Martin boundaries of $H$ coincide with those of $H/G$. A similar result is also proved in the setting of exact sequences of C$^*$-tensor categories. As an immediate application, we conclude that the boundaries of the duals of the group-theoretical easy quantum groups are classical.

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Sara Malacarne, Sergey Neshveyev. 2017-04-16. Probabilistic boundaries of finite extensions of quantum groups. https://doi.org/10.1142/s0219025717500266

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