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Vanishing at infinity on homogeneous spaces of reductive type

Part of: Global differential geometry Lie groups Noncompact transformation groups

Published online by Cambridge University Press:  15 April 2016

Bernhard Krötz ,
Eitan Sayag  and
Henrik Schlichtkrull
Bernhard Krötz
Affiliation:
Institut für Mathematik, Universität Paderborn, Warburger Straße 100, 33098 Paderborn, Germany email bkroetz@gmx.de
Eitan Sayag
Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, POB 653, Be’er Sheva 84105, Israel email eitan.sayag@gmail.com
Henrik Schlichtkrull
Affiliation:
Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark email schlicht@math.ku.dk
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Abstract

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Let $G$ be a real reductive group and $Z=G/H$ a unimodular homogeneous $G$ space. The space $Z$ is said to satisfy VAI (vanishing at infinity) if all smooth vectors in the Banach representations $L^{p}(Z)$ vanish at infinity, $1\leqslant p<\infty$. For $H$ connected we show that $Z$ satisfies VAI if and only if it is of reductive type.

Keywords

homogeneous spacerepresentationsmooth vector

MSC classification

Primary: 22F30: Homogeneous spaces 22E46: Semisimple Lie groups and their representations 53C35: Symmetric spaces
Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 7 , July 2016 , pp. 1385 - 1397
Copyright
© The Authors 2016 

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