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 ran...

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Veröffentlicht in:Mathematische Zeitschrift 2019-02, Vol.291 (1-2), p.395-419
Hauptverfasser: Petrecca, David, Röser, Markus
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Isotropy
Mathematics
Mathematics and Statistics
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description 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.
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subjects Isotropy
Mathematics
Mathematics and Statistics
title Irreducibility of the Laplacian eigenspaces of some homogeneous spaces
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