Abstract

We consider a family of singular infinite dimensional unitary representations of G = Sp(n, R) which are realized as sheaf cohomology spaces on an open G-orbit D in a generalized flag variety for the complexification of G. By parametrizing an appropriate space, M_D, of maximal compact subvarieties in D, we identify a holomorphic double fibration between D and M_D which we use to define a map P, often referred to as a double fibration or Penrose transform, from the representation into sections of a corresponding sheaf on M_D. Analysis of the construction of P shows that P is injective, the image of P is the kernel of a differential operator on M_D and P is an intertwining map.

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