On the restriction of Zuckerman's derived functor modules A_q(λ) to reductive subgroups

In this article, we study the restriction of Zuckerman's derived functor (g,K)-modules A_q(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 A_q'(λ') for a parabolic subalgebra q' of g', and determine their associated varieties. For the proof, we construct A_q(λ) on complex partial flag varieties by using D-modules.

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