On the τ(2)-model in the chiral Potts model and cyclic representation of the quantum group Uq(sl2)

We identify the precise relationship between the five-parameter τ(2)-family in the N-state chiral Potts model and XXZ chains with Uq(sl2)-cyclic representation. By studying the Yang-Baxter relation of the six-vertex model, we discover a one-parameter family of L-operators in terms of the quantum group Uq(sl2). When N is odd, the N-state τ(2)-model can be regarded as the XXZ chain of Uq(sl2) cyclic representations with qN=1. The symmetry algebra of the τ(2)-model is described by the quantum affine algebra Uq(sl2-hat) via the canonical representation. In general, for an arbitrary N, we show that the XXZ chain with a Uq(sl2)-cyclic representation for q2N = 1 is equivalent to two copies of the same N-state τ(2)-model. (fast track communication)