NEUTRINO OSCILLATIONS FROM DISCRETE NON-ABELIAN FAMILY SYMMETRIES

I discuss a SUSY GUT model with a non-Abelian discrete family symmetry that explains the observed hierarchical pattern of quark and lepton masses. This SO(10) x Delta(75) model predicts modified quadratic seesaw neutrino masses and mixing angles which are interesting for three reasons: (i) they offer a solution to the solar neutrino problem, (ii) the tau neutrino has the right mass for a cosmologically interesting hot dark matter candidate, and (iii) they suggest a positive result for the nu(mu) --> nu(tau) oscillation searches by the CHORUS and NOMAD Collaborations. However, the model shares some problems with many other predictive GUT models of quark and lepton masses. The predictions from well-known mass and angle relations, such as the relation lambda(b)(GUT) = lambda(tau)(GUT) fail in many cases. Attempts to correct these relations seem to lead to rather contrived models.