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Functional Equations and Fusion Matrices for the Eight Vertex Model

We derive sets of functional equations for the eight vertex model by exploiting an analogy with the functional equations of the chiral Potts model. From these equations we show that the fusion matrices have special reductions at certain roots of unity. We explicitly exhibit these reductions for the 3,4 and 5 order fusion matrices and compare our formulation with the algebra of Sklyanin.