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Tiny fluctuations of the Cosmic Microwave Background as well as variousobservable quantities obtained by spin raising and spin lowering of theeffective gravitational lensing potential of distant galaxies and galaxyclusters, are described mathematically as isotropic random sections ofhomogeneous spin and tensor bundles. We consider the three existing approachesto rigourous constructing of the above objects, emphasising an approach basedon the theory of induced group representations. Both orthogonal and unitaryrepresentations are treated in a unified manner. Several examples fromastrophysics are included.

Spectral expansions of random sections of homogeneous vector bundles