Complete set of commuting operators for N spins s with rotational and permutational symmetry

The authors consider a system of N spins s with permutational and rotational symmetry. The total spin, its z-component and the representation of the permutation group Ssub(N) provide good quantum numbers. For s>1/2 further operators are needed. The problem can be reduced to a problem of invariants in the enveloping algebra of SU(2s+1) applying a theorem of Weyl. This can be solved explicity for s=1 using a theory of Judd. For s = 3/2 two of the four missing operators are determined and for larger s some properties of the additional are shown. (Auth.)