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arXiv:hep-th/9312060 · Journal of Physics A Mathematical and General

Analytic Bethe ansatz and T-system in C2(1)vertex models

Atsuo Kuniba

Published Mar 7, 1994• 10 citations
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Abstract

Eigenvalues of the commuting family of transfer matrices are expected to obey the T-system, a set of functional relations, proposed recently. Here we obtain the solution to the T-system for C 2 (1) vertex models. They are compatible with the analytic Bethe ansatz and Yang-Baxterize the classical characters.
DOI
10.1088/0305-4470/27/5/002

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Using the most elementary methods and considerations, the solution of the star-triangle condition (a2+b2-c2)/2ab = ((a’)^2+(b’)^2-(c’))^2/2a’b’ is shown to be a necessary condition for the extension of the operator coalgebra of the six-vertex model to a bialgebra. A portion of the bialgebra acts as a spectrum-generating algebra for the algebraic Bethe ansatz, with which higher-dimensional representations of the bialgebra can be constructed. The star-triangle relation is proved to be necessary for the commutativity of the transfer matrices T(a, b, c) and T(a’, b’, c’).
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