T. Kobayashi,
Discrete decomposability of the restriction of Aq(λ) with respect to reductive subgroups and its applications,
Invent. Math. 117 (1994), 181-205..

Let G'⊂G be real reductive Lie groups and q a θ-stable parabolic subalgebra of Lie(G)⊗C. This paper offers a sufficient condition on (G, G', q) that the irreducible unitary representation Aq of G with non-zero continuous cohomology splits into a discrete sum of irreducible unitary representations of a subgroup G', each of finite multiplicity. As an application to purely analytic problems, new results on discrete series are also obtained for some pseudo-Riemannian (non-symmetric) spherical homogeneous spaces, which fit nicely into this framework. Some explicit examples of a decomposition formula are also found in the cases where An is not necessarily a highest weight module.
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