Z₄-symmetric factorized S-matrix in two space-time dimensions

The factorized S-matrix with internal symmetry Z₄ is constructed in two space-time dimensions. The two-particle amplitudes are obtained by means of solving the factorization, unitarity and analyticity equations. The solution of factorization equations can be expressed in terms of elliptic functions. The S-matrix contains the resonance poles naturally. The simple formal relation between the general factorized S-matrices and the Baxter-type lattice transfer matrices is found. In the sense of this relation the Z₄-symmetric S-matrix corresponds to the Baxter transfer matrix itself.