Asymptotic Schur orthogonality in hyperbolic groups with application to\n monotony

2016/10/19 by Adrien Boyer, Boyer, Adrien, Łukasz Garncarek +1 · 1 citation
Mathematics · #20C15 #20F65 #22D10 #22D25 #22D40 (Primary) #37A25 #37A30 #37A55 (Secondary) #Advanced Algebra and Geometry #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1610.06429

openalex publication_date 2016/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a generalization of Schur orthogonality relations for certain\nclasses of representations of Gromov hyperbolic groups. We apply the obtained\nresults to show that representations of non-abelian free groups associated to\nthe Patterson-Sullivan measures corresponding to a wide class of invariant\nmetrics on the group are monotonous in the sense introduced by Kuhn and Steger.\nThis in particular includes representations associated to harmonic measures of\na wide class of random walks.\n

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