Algebraic properties of an integrable t-J model with impurities

We investigate the algebraic structure of a recently proposed integrable $t-J$ model with impurities. Three forms of the Bethe ansatz equations are presented corresponding to the three choices for the grading. We prove that the Bethe ansatz states are highest weight vectors of the underlying $gl(2\mathrm{\mid }1)$ supersymmetry algebra. By acting with the $gl(2\mathrm{\mid }1)$ generators we construct a complete set of states for the model.