  We characterize the angular polyspectra, of arbitrary order, associated with
isotropic fields defined on the sphere S^2. Our techniques rely heavily on
group representation theory, and specifically on the properties of Wigner
matrices and Clebsch-Gordan coefficients. The findings of the present paper
constitute a basis upon which one can build formal procedures for the
statistical analysis and the probabilistic modelization of the Cosmic Microwave
Background radiation, which is currently a crucial topic of investigation in
cosmology. We also outline an application to random data compression and
"simulation" of Clebsch-Gordan coefficients.
