GL3-invariant solutions of the Yang-Baxter equation and associated quantum systems

GL₃-invariant, finite-dimensional solutions of the Yang-Baxter equations acting in the tensor product of two irreducible representations of the group GL₃ are investigated. A number of relations are obtained for the transfer matrices which demonstrate the connection of representation theory and the Bethe Ansatz in GL₃-invariant models. Some of the most interesting quantum and classical integrable systems connected with GL₃-invariant solutions of the Yang-Baxter equation are presented.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 120, pp. 92–121, 1982.