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June 2017 The tempered spectrum of a real spherical space
Friedrich Knop, Bernhard Krötz, Henrik Schlichtkrull
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Acta Math. 218(2): 319-383 (June 2017). DOI: 10.4310/ACTA.2017.v218.n2.a3


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.


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Friedrich Knop. Bernhard Krötz. Henrik Schlichtkrull. "The tempered spectrum of a real spherical space." Acta Math. 218 (2) 319 - 383, June 2017.


Received: 30 September 2015; Revised: 12 August 2016; Published: June 2017
First available in Project Euclid: 31 January 2018

zbMATH: 1381.22010
MathSciNet: MR3733102
Digital Object Identifier: 10.4310/ACTA.2017.v218.n2.a3

Rights: Copyright © 2017 Institut Mittag-Leffler


Vol.218 • No. 2 • June 2017
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