PENROSE TRANSFORM FOR INDEFINITE GRASSMANN MANIFOLDS

Abstract

We construct the Radon–Penrose transform as an intertwining operator of the indefinite unitary group U(p,q), from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of positive k-planes to the space of holomorphic functions over the bounded symmetric domain. We prove that the Penrose transform is injective, and that its image is exactly the space of global holomorphic solutions to the system of partial differential equations of determinant type of size k + 1.