The edge-of-wedge type embeddings of dereived functor modules for the type A classical groups

A holomorphic discrete series can be realized as the space of the holomorphic sections of a homogeneous vector bundle on a bounded symmetric domain. We can embed it into a degenerate principal series realized as the space of hyperfunction sections of a vector bundle on the Shilov boundary by taking the boundary value. We consider an algebraic version of higher cohomological analogue of such an embedding for complex reductive groups and classical groups of type A.