2017/04/30 by Sara Malacarne, Sergey Neshveyev · 1 citation
Mathematics · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Dual polyhedron #Geometric and Algebraic Topology #Group (periodic table) #Harmonic function #Invariant (physics) #Poisson distribution #Probabilistic logic #Quantum #Quantum algorithm #Quantum walk #math.OA #math.PR #math.QA
paper · pdf · doi:10.1142/s0219025717500266
published in Infinite Dimensional Analysis Quantum Probability and Related Topics 20(04), 1750026 (World Scientific) · 9 pages; v2: minor corrections
openalex created_date 2017/04/28 · openalex publication_date 2017/12/01 · arxiv created 2021/06/08 · arxiv updated 2021/06/09 · openalex updated_date 2026/08/05
Given a discrete quantum group [Formula: see text] with a finite normal quantum subgroup [Formula: see text], we show that any positive, possibly unbounded, harmonic function on [Formula: see text] with respect to an irreducible invariant random walk is [Formula: see text]-invariant. This implies that, under suitable assumptions, the Poisson and Martin boundaries of [Formula: see text] coincide with those of [Formula: see text]. A similar result is also proved in the setting of exact sequences of C[Formula: see text]-tensor categories. As an immediate application, we conclude that the boundaries of the duals of the group-theoretical easy quantum groups are classical.