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TEMPERED HOMOGENEOUS SPACES IV

Part of: Abstract harmonic analysis Noncompact transformation groups

Published online by Cambridge University Press:  07 June 2022

Yves Benoist Open the ORCID record for Yves Benoist [Opens in a new window]  and
Toshiyuki Kobayashi
Yves Benoist*
Affiliation:
Department of Mathematics, CNRS-Université Paris-Saclay, Bâtiment 307 91405, Orsay, France
Toshiyuki Kobayashi
Affiliation:
Graduate School of Mathematical Sciences and Kavli IPMU (WPI), The University of Tokyo, Komaba, 153-8914 Japan ([email protected])
*
[email protected]
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Abstract

Let G be a complex semisimple Lie group and H a complex closed connected subgroup. Let and be their Lie algebras. We prove that the regular representation of G in $L^2(G/H)$ is tempered if and only if the orthogonal of in contains regular elements by showing simultaneously the equivalence to other striking conditions, such as has a solvable limit algebra.

Keywords

tempered unitary representationsLie groupsLie algebrashomogeneous spaces

MSC classification

Primary: 43A85: Analysis on homogeneous spaces
Secondary: 22F30: Homogeneous spaces
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 6 , November 2023 , pp. 2879 - 2906
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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