GRADUATE SCHOOL OF MATHEMATICAL SCIENCES KOMABA, TOKYO, JAPAN CLASSIFICATION OF DISCRETELY DECOMPOSABLE Aq(λ) 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 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.