ON THE RESTRICTION OF ZUCKERMAN’S DERIVED FUNCTOR MODULES Aq(λ) TO REDUCTIVE SUBGROUPS

In this article, we study the restriction of Zuckerman’s derived functor (g,K)-modules Aq(λ) to g′ for symmetric pairs of reductive Lie algebras (g, g′). When the restriction decomposes into irreducible (g′,K′)-modules, we give an upper bound for the branching law. In particular, we prove that each (g′,K′)-module occurring in the restriction is isomorphic to a submodule of Aq′ (λ ′) for a parabolic subalgebra q′ of g′, and determine their associated varieties. For the proof, we realize Aq(λ) on complex partial flag varieties by using D-modules.