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[ 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 ]
The original publication is available at www.springerlink.com.
© Toshiyuki Kobayashi