Fusion operators in the generalized τ(2)-model and root-of-unity symmetry of the XXZ spin chain of higher spin**In this paper, the term ‘XXZ spin chain’ means a lattice model with the L-operator associated with the trigonometric R-matrix of the ice-type model. The ‘XXZ spin chain of higher spin’ here is named as the ‘XXZ Heisenberg model with arbitrary spin’ in [31

Abstract

We construct the fusion operators in the generalized τ(2)-model using the fused L-operators, and verify the fusion relations with the truncation identity. The algebraic Bethe-ansatz discussion is conducted on two special classes of τ(2) which include the superintegrable chiral Potts model. We then perform the parallel discussion on the XXZ spin chain at roots of unity, and demonstrate that the sl2-loop-algebra symmetry exists for the root-of-unity XXZ spin chain with a higher spin, where the evaluation parameters for the symmetry algebra are identified by the explicit Fabricius–McCoy current for the Bethe states. Parallels are also drawn to the comparison with the superintegrable chiral Potts model.