Let Γ be a Gromov hyperbolic group, endowed with an arbitrary left-invariant hyperbolic metric, quasi-isometric to a word metric. The action of Γ on its boundary ∂Γ endowed with the Patterson-Sullivan measure µ, after an appropriate normalization, gives rise to a faithful unitary representation of Γ on L 2 (∂Γ, µ). We show that these representations are irreducible, and give criteria for their unitary equivalence in terms of the metrics on Γ. Special cases include quasi-regular representations on the Poisson boundary.
ABSTRACT. The Hecke algebra C q [W] of a Coxter group W, associated to parameter q, can be completed to a von Neumann algebra N q (W). We study such algebras in case where W is right-angled. We determine the range of q for which N q (W) is a factor, i.e. has trivial center. Moreover, in case of nontrivial center, we prove a result allowing to decompose N q (W) into a finite direct sum of factors.
In this paper we present our work in progress on building an artificial intelligence system dedicated to tasks regarding the processing of formal documents used in various kinds of business procedures. The main challenge is to build machine learning (ML) models to improve the quality and efficiency of business processes involving image processing, optical character recognition (OCR), text mining and information extraction. In the paper we introduce the research and application field, some common techniques used in this area and our preliminary results and conclusions.
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 non-abelian free groups associated to the Patterson-Sullivan measures corresponding to a wide class of invariant metrics on the group are monotonous in the sense introduced by Kuhn and Steger. This in particular includes representations associated to harmonic measures of a wide class of random walks.
We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.2010 Mathematics Subject Classification. 57S20, 22A25.
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