  For a Hermitian Lie group $G$, we study the family of representations induced
from a character of the maximal parabolic subgroup $P=MAN$ whose unipotent
radical $N$ is a Heisenberg group. Realizing these representations in the
non-compact picture on a space $I(\nu)$ of functions on the opposite unipotent
radical $\bar{N}$, we apply the Heisenberg group Fourier transform mapping
functions on $\bar N$ to operators on Fock spaces. The main result is an
explicit expression for the Knapp-Stein intertwining operators $I(\nu)\to
I(-\nu)$ on the Fourier transformed side. This gives a new construction of the
complementary series and of certain unitarizable subrepresentations at points
of reducibility. Further auxiliary results are a Bernstein-Sato identity for
the Knapp-Stein kernel on $\bar{N}$ and the decomposition of the metaplectic
representation under the non-compact group $M$.
