Irreducibility of these representations is established in a standard way. Each representation breaks up as a direct sum of one dimensional eigenspaces of the rotation group each of which is generated by a C vector for the whole group. It follows that any closed invariant subspace is generated by the algebraic direct sum of eigenspaces it contains and that this sum is invariant under the infinitesimal action of the Lie algebra g . On the other hand, that action is irreducible.