Irreducibility of the Laplacian eigenspaces of some homogeneous spaces

David Petrecca; Markus Roeser

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arXiv · 1707.01403

Irreducibility of the Laplacian eigenspaces of some homogeneous spaces

David Petrecca·Markus Roeser

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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.

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BibTeX RIS

David Petrecca, Markus Roeser. 2017-07-05. Irreducibility of the Laplacian eigenspaces of some homogeneous spaces. https://arxiv.org/abs/1707.01403

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