  Let $G/K$ be an irreducible Hermitian symmetric spaces of compact type with
the standard homogeneous complex structure. Then the real symplectic manifold
$(T^*(G/K),\Omega)$ has the natural complex structure $J^-$. We construct all
$G$-invariant K\"ahler structures $(J,\Omega)$ on homogeneous domains in
$T^*(G/K)$ anticommuting with $J^-$. Each such a hypercomplex structure,
together with a suitable metric, defines a hyperk\"ahler structure. As an
application, we obtain a new proof of the Harish-Chandra and Moore theorem.
