Invariant hyperkahler 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 Kahler 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 hyperkahler structure. As an application, a new proof of the theorem of Harish-Chandra and Moore for Hermitian symmetric spaces is obtained.