Invariant hyperkähler structures on the cotangent bundles of Hermitian symmetric spaces

Abstract

Let be an irreducible Hermitian symmetric space of compact type with standard homogeneous complex structure. Then the real symplectic manifold has the natural complex structure . All -invariant Kéhler structures on -invariant subdomains of anticommuting with 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.