The transfer matrix of a superintegrable chiral Potts model as theQoperator of root-of-unity XXZ chain with cyclic representation of U ₐ (sl₂)

We demonstrate that the transfer matrix of the inhomogeneous N-state chiral Potts model with two vertical superintegrable rapidities serves as the Q-operator of XXZ chain model for a cyclic representation of U ₐ (sl₂) with Nth root-of-unity q and representation-parameter for odd N. The symmetry problem of XXZ chain with a general cyclic U ₐ (sl₂) -representation is mapped onto the problem of studying Q-operator of some special one-parameter family of generalized ^ (2) -models. In particular, the spin-N-12 XXZ chain model with qN=1 and the homogeneous N-state chiral Potts model at a specific superintegrable point are unified as one physical theory. By Baxter's method developed for producing Q₇₂-operator of the root-of-unity eight-vertex model, we construct the QR, QL- and Q-operators of a superintegrable ^ (2) -model, then identify them with transfer matrices of the N-state chiral Potts model for a positive integer N. We thus obtain a new method of producing the superintegrable N-state chiral Potts transfer matrix from the ^ (2) -model by constructing its Q-operator.