Volume 218 (2017)
The tempered spectrum of a real spherical space
Pages: 319 – 383
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.
The second author was supported by ERC Advanced Investigators Grant HARG 268105.
Received 30 September 2015
Received revised 12 August 2016
Published 27 November 2017