Killing tensor fields on the standard sphere and spectra of \(SO(n+1)/SO(n-1)\times SO(2)\) and \(O(n+1)/O(n-1)\times O(2)\)
The goal of this paper is to exhibit the eigen-space decomposition for the Laplacian of the Grassmann manifolds in the title (with their canonical Riemannian metrics) and to clarify their relation to the eigen- space decomposition of the Lichnerowicz operator on the standard sphere \((S^ n,g_ 0)\) when restricted to the symmetric tensor algebra generated by the Killing vector fields.
scientific article; zbMATH DE number 3848183