  The holomorphic homogeneous prepotential encoding the special geometry of the
special K\"ahler manifolds ${\textstyle SU(1,n)\over \textstyle U(1)\otimes
SU(n)}$ is constructed using the symplectic embedding of the isometry group
$SU(1,n)$ into $Sp(2n+2,{\hbox{\bf R}})$. Also the automorphic functions of
these manifolds are discussed.
