T. Kobayashi,

*Discrete series representations for the orbit spaces arising
from two involutions of real reductive Lie groups*,

J. Funct. Anal.**152** (1998), 100-135..

J. Funct. Anal.

Let[ preprint version(dvi) | ScienceDirect | ZMath ]H⊂Gbe real reductive Lie groups. A discrete series representation for a homogeneous spaceG/His an irreducible representation ofGrealized as a closedG-invariant subspace ofL^{2}(G/H). The condition for the existence of discrete series representations forG/Hwas not known in general except for reductive symmetric spaces. This paper offers a sufficient condition for the existence of discrete series representations forG/Hin the setting thatG/His a homogeneous submanifold of a symmetric space \tilde{G}/\tilde{H} whereG⊂\tilde{G} ⊃\tilde{H}. We prove that discrete series representa-tions are non-empty for a number of non-symmetric homogeneous spaces such asSp(2n,R)/Sp(n_{0},C)×GL(n_{1},C)×...×GL(n_{k},C) (n_{j}=n) andO(4m,n)/U(2m,j) (0≤2j≤n).

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

© Toshiyuki Kobayashi