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Irreducibility of the Laplacian eigenspaces of some homogeneous spaces (1707.01403v2)
Published 5 Jul 2017 in math.DG, math.RT, and math.SP
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.