Representations and Mass Formulas for SU(4)

A hierarchial scheme of $\mathrm{SU}\mathrm{}\left(n\right)\mathrm{}$ symmetries among the strong interactions is proposed with the $n-1\mathrm{}$ additive quantum numbers exactly conserved. Simple dynamics as well as mass-splitting considerations are shown to favor the assignment of the measons to the 15-dimensional representations and the baryons and ${\frac{3}{2}}^{+}$ isobars to two inequivalent 20-dimensional representations of SU(4). The predictions of new particles are discussed.