Extended weak isospin and fermion masses in a unified model

It is interesting to ask whether the weak-isospin gauge group ${\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_L$ is embedded in a larger symmetry group. From a model-building perspective there are usually too many possible answers to this question, because extensions invariably introduce new gauge anomalies. New fermions then have to be postulated, usually in an ad hoc manner, to cancel these anomalies. However, the quark-lepton symmetric models of Foot and Lew allow one to extend the weak-isospin group in a disciplined way, because the new anomalies can now cancel between quarks and generalized leptons. The basics of a model with gauge group $G={\left[\mathrm{SU}\mathrm{}\right(3\left)\right]}^4$ are presented in this paper. We find that, through left-right symmetry, a partial unification of the gauge coupling constants of the theory naturally suggests itself. We also find that the symmetries of the model can impose restrictions on fermion masses and mixing angles at the tree level, which renormalization effects and mixing phenomena may modify in a predictive manner.