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 approximati on) of the group is found. With the help of the modified group projector te chnique, this result is applied to a system of identical particles with spi n-independent interaction, to derive the Dirac-Heisenberg Hamiltonian and i ts effective space for arbitrary orbital occupation numbers and arbitrary s pin. This gives transparent insight into the physical contents of this Hami ltonian, showing that formal generalizations with spin greater than 1/2 inv olve non-trivial additional physical assumptions.