A Plancherel formula for L^2(G/H) for almost symmetric subgroups
  In this paper we study the Plancherel formula for a new class of homogeneous spaces for real reductive Lie groups; these spaces are fibered over non-Riemannian symmetric spaces, and they exhibit a phenomenon of uniform infinite multiplicities. They also provide examples of non-tempered representations of the group appearing in the Plancherel formula. Several classes of examples are given. 
Bent Orsted and Birgit Speh
math.RT