The Onsager Algebra Symmetry of $\tau^{(j)}$-matrices in the Superintegrable Chiral Potts Model

Abstract

We demonstrate that the $\tau^{(j)}$-matrices in the superintegrable chiral Potts model possess the Onsager algebra symmetry for their degenerate eigenvalues. The Fabricius-McCoy comparison of functional relations of the eight-vertex model for roots of unity and the superintegrable chiral Potts model has been carefully analyzed by identifying equivalent terms in the corresponding equations, by which we extract the conjectured relation of $Q$-operators and all fusion matrices in the eight-vertex model corresponding to the $T\hat{T}$-relation in the chiral Potts model.