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 A(q)(lambda) 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')(lambda') for a parabolic subalgebra q' of g', and determine their associated varieties. For the proof, we realize A(q)(lambda) on complex partial flag varieties by using D-modules.