(ZNX)N-1 GENERALIZATION OF THE CHIRAL POTTS-MODEL

We show that the R-matrix which intertwines two n-by-N(n-1) state cyclic L-operators related with a generalization of U(q)(sl(n)) algebra can be considered as a Boltzmann weight of four-spin box for a lattice model with two-spin interaction just as the R-matrix of the checkerboard chiral Potts model. The rapidity variables lie on the algebraic curve of the genus g = N2(n-1)(n-1)N-n)+1 defined by 2n-3 independent moduli. This curve is a natural generalization of the curve which appeared in the chiral Potts model. Factorization properties of the L-operator and its connection to the SOS models are also discussed.