Localization of cohomologically induced modules to partial flag varieties

Cohomological induction gives an algebraic method for constructing representations for a real reductive Lie group G from irreducible representations of reductive subgroups. Beilinson-Bernstein Localization alternatively gives a geometric method for constructing Harish-Chandra modules for G, with a fixed infinitessimal character, from some specific representations of a Cartan subgroup which depend on the character. The duality theorem of Hecht, Milicic, Schmid and Wolf establishes a relationship between modules cohomologically induced from a Cartan and the sheaf cohomology of the D-modules on the complex flag variety for G determined by the Beilinson-Berstein construction. The main results of this thesis give a generalization of the duality theorem to partial flag varieties, which recovers cohomologically induced modules arising from larger reductive subgroups.