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

AbstractWe give a classification of the triples (g,g′,q) such that Zuckerman’s derived functor (g,K)-module Aq(λ) for a θ-stable parabolic subalgebra q is discretely decomposable with respect to a reductive symmetric pair (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