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Irreducibility of the Laplacian eigenspaces of some homogeneous spaces

Irreducibility of the Laplacian eigenspaces of some homogeneous spaces For a compact homogeneous space G / K, we study the problem of existence of G-invariant Riemannian metrics such that each eigenspace of the Laplacian is a real irreducible representation of G. We prove that the normal metric of a compact irreducible symmetric space has this property only in rank one. Furthermore, we provide existence results for such metrics on certain isotropy reducible spaces. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Irreducibility of the Laplacian eigenspaces of some homogeneous spaces

Mathematische Zeitschrift , Volume 291 (2) – May 31, 2018

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-018-2088-z
Publisher site
See Article on Publisher Site

Abstract

For a compact homogeneous space G / K, we study the problem of existence of G-invariant Riemannian metrics such that each eigenspace of the Laplacian is a real irreducible representation of G. We prove that the normal metric of a compact irreducible symmetric space has this property only in rank one. Furthermore, we provide existence results for such metrics on certain isotropy reducible spaces.

Journal

Mathematische ZeitschriftSpringer Journals

Published: May 31, 2018

References