Boundary Algebraic Bethe Ansatz for a nineteen vertex model with $U_{q}[\mathrm{osp}(2|2)^{(2)}]$ symmetry

Abstract: The boundary algebraic Bethe Ansatz for a supersymmetric nineteen vertex-model constructed from a three-dimensional representation of the twisted quantum affine Lie superalgebra $U_{q}[\mathrm{osp}(2|2)^{(2)}]$ is presented. The eigenvalues and eigenvectors of Sklyanin's transfer matrix, with diagonal reflection $K$-matrices, are calculated and the corresponding Bethe Ansatz equations are obtained.