I found the following reading a paper (http://www.vsi.cs.uni-frankfurt.de/download/KrajsekVisapp06.pdf, pg 4 first column). The statement is for for compact groups:
if "a Casimir operator has the symmetry of the group G, i.e. there exists no operation which does not belong to the group and under which the Casimir operator is invariant, then its eigenfunctions are basis functions of irreducible representation (Wigner, 1959).
I cannot figure out where to find this result in the Wigner book. Is this a well konw fact? Someone can help?
Thanks!!!
Fabio
