Boundary Representations of Locally Compact Hyperbolic Groups

  • Tagungsort:

    Geb. 20.30, SR 1.067

  • Datum:

    3.12.2024

  • Referent:

    Michael Glasner

  • Zeit:

    14:00 Uhr

  • Abstract: Given a non-elementary locally compact hyperbolic group G equipped with a left invariant metric d one can define a measure on the Gromov boundary called the Patterson Sullivan measure associated to d. This measure is non-singular with respect to the G action and contains geometric information on d. I will discuss the Koopman representations of these actions and sketch a proof of their irreducibility and classification up to unitary equivalence, generalizing works of Garncarek in the discrete case. I will also describe connections with a recent work of Caprace, Kalantar and Monod on the type I property for hyperbolic groups.