T. Kobayashi,

*Discrete decomposability of the restriction of A*_{q}(λ) *with respect to reductive subgroups and its applications*,

Invent. Math.**117** (1994), 181-205..

Invent. Math.

Let[ preprint version(dvi) | full text(pdf) | SpringerLink | GDZ | ZMath | related papers ]G'⊂Gbe 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 representationA_{q}ofGwith non-zero continuous cohomology splits into a discrete sum of irreducible unitary representations of a subgroupG', 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.

The original publication is available at www.springerlink.com.

© Toshiyuki Kobayashi