Bethe ansatz equations for quantum chains combining different representations of SU(3)

The general expression for the local matrix of a quantum chain L(theta) with the site space in any representation of SU(3) is obtained. This is made by generalizing L(theta) from the fundamental representation and imposing the fulfilment of the Yang-Baxter equation. With these operators and using a generalization of the nested Bethe ansatz, the Bethe equations for a multistate quantum chain combining two arbitrary representations of SU(3) are obtained.