Localization of cohomological induction (Q355147)

Let \(G_\mathbb R\) be a connected real reductive Lie group with a Cartan involution \(\theta\) so that the group of fixed points \(K_\mathbb R\) := \((G_\mathbb R)^\theta\) is a maximal compact subgroup. Now let \(\mathfrak g\) be the complexified Lie algebra of \(G_\mathbb R\) and \(K\) the complexification of \(K_\mathbb R\). The duality theorem of Hecht, Milicic, Schmid and Wolf relates \((\mathfrak g, K)\)-modules cohomology induced from a Borel subalgebra to \(\mathcal D\)-modules on the flag variety of \(\mathfrak g\).NEWLINENEWLINEIn the present article the author extends this theorem to more general pairs in the setting of complex linear algebraic groups.