Groups and Dynamics Seminar

We discuss the problem of determining irreducibility of Koopman representations of non-singular actions. In recent years, the case of boundary actions has attracted considerable attention, following the work fo Bader-Muchnik (2011), where they proved irreducibility actions of the fundamental group of compact negatively curved Riemannian manifold, and used that to prove a rigidity resulf for such manifolds. THey conjectured that all Koopman representations associated to boundary actions are irreducible. The conjecture has been proven in several cases, however, a class of counter-examples was given by Bjorklund-Harman-Oppelmayer (2023). In this talk, we give new examples of non-singular actions with irreducible Koopman representations. These actions are generated by a non-irreducible boundary actions mentioned above, and a measure preserving action. This is joint work with Yair Hartman.