科研之友
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摘要
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. The proof for this is new but rather elementary, and we give all details. As an application we use several results from the recent literature studying possible nontemperedness of homogeneous spaces; thus we provide examples of nontempered representations of the group appearing in the Plancherel formula for our homogeneous spaces. Several classes of examples are given, each building on different techniques and new results from the theory of symmetric spaces.
- 出版日期2016-7
