  The general form of the operators commuting with the ground representation
(appearing in many physical problems within single particle approximation) of
the group is found. With help of the modified group projector technique, this
result is applied to the 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 1/2 involve nontrivial
additional physical assumptions.
