Abstract
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.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 120, pp. 92–121, 1982.
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Kulish, P.P., Reshetikhin, N.Y. GL3-invariant solutions of the Yang-Baxter equation and associated quantum systems. J Math Sci 34, 1948–1971 (1986). https://doi.org/10.1007/BF01095104
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DOI: https://doi.org/10.1007/BF01095104