The Flavor Symmetry

Assuming that the lepton, quark and Higgs fields belong to the three-dimensional reducible representation of the permutation group S_3, we suggest a minimal S_3 invariant extension of the standard model. We find that in the leptonic sector the exact S_3 X Z_2 symmetry, which allows 6 real independent parameters, is consistent with experimental data and predicts the bi-maximal mixing of the left-handed neutrinos and that the $tau$ neutrino is the lightest neutrinno. Z_2 is anomaly-free, but forbids CP-violations in the leptonic as well as in the hadronic sector. Therefore, we may identify the origin of the CP-violations with the breaking of the Z_2 symmetry, which may be understood in a more fundamental theory. With the exact S_3 only, there are 10 real independent parameters and one independent phase in the hadronic sector. A set of the values of these parameters that are consistent with the experimental observations is given.