Appears in collection : Symmetry in Geometry and Analysis

Induced representations from Heisenberg parabolic subgroups are interesting as they are related to singular or small nilpotent orbits. We study these induced representations for Hermitian Lie groups. We find the complementary and composition series. Together with Jan Frahm and Clemens Weiske we find also the non-compact realization of complementary series in terms of Weyl transform and we study related branching problems.