Algebraic Bethe ansatz for an integrable Uq[Sl(n|m)] vertex model with mixed representations

We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of Uq[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider all (n+m)!n!m! possibilities of choosing the grading for arbitrary values of n and m. This allows us to derive the transfer matrix eigenvalues and the respective Bethe ansatz equations for general grading choices.