Classification of discretely decomposable A_q(\lambda) with respect to   reductive symmetric pairs
  We give a classification of the triples (g,g',q) such that Zuckerman's derived functor (g,K)-module A_q(\lambda) for a \theta-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. 
Toshiyuki Kobayashi and Yoshiki Oshima
math.RT