Fourier coefficients of invariant random fields on homogeneous spaces of compact Lie groups

Let T be a random field invariant under the action of a compact group G. We investigate properties of the Fourier coefficients as orthogonality and Gaussianity. In particular we give conditions ensuring that independence of the random Fourier coefficients implies Gaussianity. As a consequence, in general, it is not possible to simulate a non-Gaussian invariant random field through its Fourier expansion using independent coefficients. end{abstract}