Elliptical harmonic functions on the sphere in four-dimensional complex space

Basing on the group-theoretical considerations, the most general complete set of commuting operators on the sphere in four-dimensional complex space is constructed. It is shown that this set of observables is realized for the most general parametrization of the sphere in this space using the elliptical coordinate system. The eigen-functions of this set of operators are constructed which are harmonic functions on the sphere in four-dimensional complex space and may serve as a basis for irreducible SU(4) group representations. The eigenvalues of nontrivial diagonal operators of this set were determined. Applications of results obtained to drive the mass formula for a mass of particles in SU(4) supermultiplets and the derivation of sum rules for a mass of particles are discussed