Abstract:
The talk presents several results by Bachir Bekka and Pierre de la Harpe on group representations of a group G acting on a reproducing kernel Hilbert space H of functions on a set X. In partcular, it is shown that for the irreducibility of the representation it is enough to check that the space of K-invariant functions in H is one-dimensional, where K is the isotropy group in G of some point in X. Several examples will be given, including the holomorphic discrete series representations on the (weighted) Bergman space on the unit disk.