On the SO(7) symmetry of the SO(8) monopole and quadrupole pairing model

The SO(7) D-pairing symmetry of the SO(8) monopole and quadrupole pairing model is shown to be unusual in that there is no corresponding group generated only by number-conserving operators. Rather, the SO(7) symmetry is manifested in terms of number-conserving operators only by taking a particular combination of the Casimir operators appropriate for the other subgroup chains.