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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Asymptotic Schur orthogonality in hyperbolic groups with application to monotony


Authors: Adrien Boyer and Łukasz Garncarek
Journal: Trans. Amer. Math. Soc. 371 (2019), 6815-6841
MSC (2010): Primary 20C15, 20F65, 22D10, 22D40; Secondary 22D25, 37A25, 37A30, 37A55
DOI: https://doi.org/10.1090/tran/7653
Published electronically: February 20, 2019
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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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Additional Information

Adrien Boyer
Affiliation: Weizmann Institute of Science, Herzl Street 234, Rehovot 7610001, Israel
Email: aadrien.boyer@gmail.com

Łukasz Garncarek
Affiliation: Weizmann Institute of Science, Herzl Street 234, Rehovot 7610001, Israel
Email: lukgar@gmail.com

DOI: https://doi.org/10.1090/tran/7653
Keywords: Hyperbolic group, boundary representation, Schur orthogonality, property RD, Patterson--Sullivan measure, Gibbs measures, equidistribution
Received by editor(s): August 29, 2017
Published electronically: February 20, 2019
Additional Notes: The first author was partially supported by ERC Grant 306706.
Article copyright: © Copyright 2019 American Mathematical Society