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Based on the rational R-matrix of the supersymmetric sl(2,1) matrixdifference equations are solved by means of a generalization of the nestedalgebraic Bethe ansatz. These solutions are shown to be of highest-weight withrespect to the underlying graded Lie algebra structure.Comment: 10 pages, LaTex, references and acknowledgements added, spl(2,1) now  called sl(2,1

Matrix difference equations for the supersymmetric Lie algebrasl(2,1) and the `off-shell' Bethe ansatz