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

TL;DR

This paper investigates the spectral properties of generalized Laplacians on compact homogeneous spaces, revealing how their spectra depend on hidden symmetries and G-invariant metrics.

Contribution

It establishes the spectral framework for generalized Laplacians on homogeneous spaces, highlighting the role of hidden symmetries and G-isometries in spectral configurations.

Findings

Spectral configuration depends on G-isometries.

Hidden symmetries influence the spectral setting.

Results apply to generic G-invariant metrics.

Abstract

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 $M=G/K$. 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.