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We construct the fusion operators in the generalized $\tau^{(2)}$-model usingthe fused $L$-operators, and verify the fusion relations with the truncationidentity. The algebraic Bethe ansatz discussion is conducted on two specialclasses of $\tau^{(2)}$ which include the superintegrable chiral Potts model.We then perform the parallel discussion on the XXZ spin chain at roots ofunity, and demonstrate that the $sl_2$-loop-algebra symmetry exists for theroot-of-unity XXZ spin chain with a higher spin, where the evaluationparameters for the symmetry algebra are identified by the explicitFabricius-McCoy current for the Bethe states. Parallels are also drawn to thecomparison with the superintegrable chiral Potts model.Comment: Latex 33 Pages; Typos and errors corrected, New improved version by  adding explanations for better presentation. Terminology in the content and  the title refined. References added and updated-Journal versio

Fusion operators in the generalized τ(2)-model and root-of-unity symmetry of theXXZspin chain of higher spin

Fusion operators in the generalized τ⁽²⁾-model and root-of-unity symmetry of theXXZspin chain of higher spin