The spectrum of an open vertex model based on the Uq[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the Uq[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables.