S_3 Symmetry and Neutrino Masses and Mixings
  Based on a universal seesaw mass matrix model with three scalars \phi_i, and by assuming an S_3 flavor symmetry for the Yukawa interactions, the lepton masses and mixings are investigated systematically. In order to understand the observed neutrino mixing, the charged leptons (e, \mu, \tau) are regarded as the 3 elements (e_1, e_2, e_3) of S_3, while the neutrino mass-eigenstates are regarded as the irreducible representation (\nu_\eta, \nu_\sigma, \nu_\pi) of S_3, where (\nu_\pi, \nu_\eta) and \nu_\sigma are a doublet and a singlet, respectively, which are composed of the 3 elements (\nu_1, \nu_2, \nu_3) of S_3. 
Yoshio Koide