  In his article "Unitary Representations and Complex Analysis", David Vogan
gives a characterization of the continuous invariant Hermitian forms defined on
the compactly supported sheaf cohomology groups of certain homogeneous analytic
sheaves defined on open orbits in generalized flag manifolds. In the last
section of the manuscript, Vogan raises a question about the possibility of a
topological Frobenius reciprocity for these representations. In this article we
give a specific version of the topological reciprocity in the regular,
antidominant case and use it to study the existence of continuous invariant
hermitian forms on the sheaf cohomology. In particular, we obtain a natural
relationship between invariant forms on the sheaf cohomology and invariant
forms on the geometric fiber.
