Abstract
Let $G/H$ be a unimodular real spherical space which is either absolutely spherical, i.e. the real form of a complex spherical space, or of wave-front type. It is shown that every tempered representation for $G/H$ embeds into a twisted discrete series for a boundary degeneration of $G/H$. If $G/H$ is of wave-front type it follows that the tempered representation is parabolically induced by a twisted discrete series representation for a real spherical space formed by a Levi subgroup.
Funding Statement
The second author was supported by ERC Advanced Investigators Grant HARG 268105.
Citation
Friedrich Knop. Bernhard Krötz. Henrik Schlichtkrull. "The tempered spectrum of a real spherical space." Acta Math. 218 (2) 319 - 383, June 2017. https://doi.org/10.4310/ACTA.2017.v218.n2.a3
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