Hidden symmetries and the generic spectral setting of generalized laplacians on homogeneous spaces

The purpose of this work is to establish the spectral setting of some generalized Laplace operators associated to a generic $G$-invariant metric on a compact homogeneous space $M=G\mathrm{/}K$. We show that this generic spectral configuration depends on the $G$-isometries and on some certain hidden symmetries constructed in the adjacent structures of $M$ and of these operators.