  Tiny fluctuations of the Cosmic Microwave Background as well as various
observable quantities obtained by spin raising and spin lowering of the
effective gravitational lensing potential of distant galaxies and galaxy
clusters, are described mathematically as isotropic random sections of
homogeneous spin and tensor bundles. We consider the three existing approaches
to rigourous constructing of the above objects, emphasising an approach based
on the theory of induced group representations. Both orthogonal and unitary
representations are treated in a unified manner. Several examples from
astrophysics are included.
