Invariant hyperkahler structures on the cotangent bundles of Hermitian symmetric spaces

Let $G\mathrm{/}K$ be an irreducible Hermitian symmetric spaces of compact type with the standard homogeneous complex structure. Then the real symplectic manifold $(T^{\ast }(G\mathrm{/}K),\mathrm{\Omega })$ has the natural complex structure $J^{-}$. We construct all $G$-invariant K"ahler structures $(J,\mathrm{\Omega })$ on homogeneous domains in $T^{\ast }(G\mathrm{/}K)$ 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.