Harmonics and spectra on general coset manifolds

The authors present a general method to compute, for any compact reductive coset manifold, the spectrum of scalars., vectors, spinors, etc. Much was already known on this subject, and much has been discovered during the last three years in the course of work on Kaluza-Klein supergravity. In particular they mention the general discussion and the subsequent practical calculational methods. Their aim in this contribution has been to givve a comprehensive and systematic derivation of spectra,and to work through an example which is both not too trivial nor too complicated