The final talk in this series will construct examples for Hilbert modules of cohomology, starting from the Narasimhan-Okamoto realization of the discrete series, but improving their presentation in a more conceptual manner. The holomorphic discrete series will of course be included as a basic example. Even for the unit ball (or rank 1) we obtain large classes of Hilbert modules beyond the holomorphic setting. If time permits, we also discuss the basic cases of higher rank symmetric domains, for example the unit ball of symmetric r-by-r matrices.
