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

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

2011-07-14

arxiv.org/abs/1107.2833v1

Mathematics

Representation Theory

30 pages

Scientific paper

In this paper, 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 construct A_q(\lambda)-modules on complex partial flag varieties by using D-modules.

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