Abstract
We consider solutions to the reflection equation for the critical Z N -symmetric vertex model, which is the trigonometric limit of the elliptic Z N -symmetric R-matrix of Belavin. These critical R-matrices have two parameters u and η. The transfer matrices T(u, η) constructed from this R-matrix R(u, η) under the cyclic boundary condition are commutative among different u when η is in common, [T(u, η), T(v, η)] = 0. We prove that an arbitrary solution to the reflection equation is independent of the parameter η.
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