Asymptotic Schur orthogonality in hyperbolic groups with application to monotony

Boyer, Adrien; Garncarek, Łukasz

doi:10.1090/tran/7653

Asymptotic Schur orthogonality in hyperbolic groups with application to monotony
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by Adrien Boyer and Łukasz Garncarek PDF

Trans. Amer. Math. Soc. 371 (2019), 6815-6841 Request permission

Abstract:

We prove a generalization of Schur orthogonality relations for certain classes of representations of Gromov hyperbolic groups. We apply the obtained results to show that representations of nonabelian free groups associated with the Patterson–Sullivan measures corresponding to a wide class of invariant metrics on the group are monotonic in the sense introduced by Kuhn and Steger. This in particular includes representations associated with harmonic measures of a wide class of random walks.

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