Supermultiplet approach to relativistic equations

The relativistic equations for a particle with an arbitrary spin have SU(4) symmetry. In the general case, the SU(4) --> SU(2) x SU(2) supermultiplet formalism gives a reducible set of relativistic equations. To obtain an irreducible set, it is necessary to use a basis adopted to another subgroup chain: SU(4) subset of Sp(4) subset of U(1) x SU(2), where SU(2) is a usual spin group and U(1) is generated by the third projection T-3 Of the sign-spin. The structure of this basis is discussed. It is shown that the algebraic results developed earlier in the nuclear-shell model are useful in solving the relativistic problems under consideration.