Mass Matrix Model Broken From A 4 To 2 ↔ 3 Symmetry Takeshi FUKUYAMA

2↔3 symmetry is realized by the breaking from alterating group of degree 4 (A4) symmetry. A4 explains why the generation number is three. However the mass matrices are realized in the form of the breaking to 2 ↔ 3 symmetry ×Z3, which leads us to 2 ↔ 3 symmetric mass matrix with vanishing (1,1) component. Thus the 3 × 3 mass matrix model with 2 ↔ 3 symmetry and vanishing (1,1) component has the group theoretical background as the symmetry in GUT model.