Invariant hyperkähler structures on the cotangent bundles of Hermitian symmetric spaces

Let $G/K$ be an irreducible Hermitian symmetric space of compact type with standard homogeneous complex structure. Then the real symplectic manifold $(T^*(G/K),\Omega)$ has the natural complex structure $J^-$. All $G$-invariant Kéhler structures $(J,\Omega)$ on $G$-invariant subdomains of $T^*(G/K)$ anticommuting with $J^-$ are constructed. Each hypercomplex structure of this kind, equipped with a suitable metric, defines a hyperkéhler structure. As an application, a new proof of the theorem of Harish-Chandra and Moore for Hermitian symmetric spaces is obtained.