  For a symmetric $R$-space $K/L=G/P$ the standard intertwining operators
provide a canonical $G$-invariant pairing between sections of line bundles over
$G/P$ and its opposite $G/\overline{P}$. Twisting this pairing with an
involution of $G$ which defines a non-compactly causal symmetric space $G/H$ we
obtain an $H$-invariant form on sections of line bundles over $G/P$.
Restricting to the open $H$-orbits in $G/P$ constructs the Berezin forms
studied previously by G. van Dijk, S. C. Hille and V. F. Molchanov. We
determine for which $H$-orbits in $G/P$ and for which line bundles the Berezin
form is positive semidefinite, and in this case identify the corresponding
representations of the dual group $G^c$ as unitary highest weight
representations. We further relate this procedure of passing from
representations of $G$ to representations of $G^c$ to reflection positivity.

Representation Theory