Classification of discretely decomposable Aq(λ)Aq(λ) with respect to reductive symmetric pairs

We give a classification of the triples (g,g′,q)(g,g′,q) such that Zuckerman’s derived functor (g,K)(g,K)-module Aq(λ)Aq(λ) for a θθ-stable parabolic subalgebra qq is discretely decomposable with respect to a reductive symmetric pair (g,g′)(g,g′). The proof is based on the criterion for discretely decomposable restrictions by the first author and on Berger’s classification of reductive symmetric pairs.