ELEMENTARY FERMIONS AND SU(2/1) REPRESENTATIONS

A single generation of leptons (quarks) can be described by the smallest irreducible non-typical (typical) representation of the Lie superalgebra SU (2/1). Here, the "super" qualifier should be understood as a reference to left-right parity (it is a Z2 symmetry). The smallest reducible indecomposable representations of this Lie superalgebra are of several types. One describes the mixing of each leptonic generation with a corresponding right neutrino. Another describes either the coupling between generations of extended leptonic representations of the previous kind or the coupling between generations of quarks. In this last case the hyper-charge generator is not diagonal. In the indecomposable cases, the particular structure of the Yukawa couplings allows one to find constraints between masses and mixing matrices (for instance a relation between Cabibbo angle and quark masses). The generalized Yang-Mills field incorporating the Z2 left-right gauge freedom contains both usual Yang-Mills fields of SU (2) X U (1) and a doublet of Higgs fields. It is already known that the square of its curvature gives the lagrangian describing the bosonic sector of the standard model.