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.[ preprint version(dvi) | full text(pdf) | SpringerLink | GDZ | ZMath | related papers ]
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© Toshiyuki Kobayashi