A Plancherel formula for L^2(G/H) for almost symmetric subgroups

TL;DR

This paper develops a Plancherel formula for a novel class of homogeneous spaces associated with real reductive Lie groups, revealing uniform infinite multiplicities and non-tempered representations, with multiple examples provided.

Contribution

It introduces a Plancherel formula for fibered homogeneous spaces over non-Riemannian symmetric spaces, highlighting new phenomena like infinite multiplicities and non-tempered representations.

Findings

Spaces exhibit uniform infinite multiplicities

Non-tempered representations appear in the Plancherel formula

Multiple classes of examples are provided

Abstract

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.