T. Kobayashi and Y. Oshima, Classification of discretely decomposable Aq(λ) with respect to reductive symmetric pairs, Advances in Mathematics 231 (2012), 2013-2047, arXiv:1104.4400. DOI:10.1016/j.aim.2012.07.006..

We 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.

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