Group projector generalization of the Dirac-Heisenberg model

The general form of the operators commuting with the ground representation (appearing in many physical problems within the single-particle approximation) of the group is found. With the help of the modified group projector technique, this result is applied to a system of identical particles with spin-independent interaction, to derive the Dirac-Heisenberg Hamiltonian and its effective space for arbitrary orbital occupation numbers and arbitrary spin. This gives transparent insight into the physical contents of this Hamiltonian, showing that formal generalizations with spin greater than ½ involve non-trivial additional physical assumptions.