Factorizable S-Matrix and Symmetry Operator With Toroidal Rapidity Values

We constructed the factorizable S-matrix and obtained the symmetry operator which commutes with the S-matrix and has a new form of "coproduct",the elements of which depend on the parameters defining the toroidal rapidity surface.By defining a new operator which commutes with the symmetry operator the Yang-Baxter equation can be obtained.Finally,the relation between the broken Z_N symmetric model and the chiral Potts model was expressed explicitly in the selfdual genus zero limit.