Cohomology of Standard Modules on Partial Flag Varieties

Cohomological induction gives an algebraic method for constructing representations of 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 from certain representations of a Cartan subgroup. The duality theorem of Hecht, Miličić, Schmid and Wolf establishes a relationship between modules cohomologically induced from minimal parabolics and the cohomology of the D-modules on the complex flag variety for G determined by the BeilinsonBernstein construction. The main results of this paper give a generalization of the duality theorem to partial flag varieties, which recovers cohomologically induced modules arising from nonminimal parabolics.