Abstract
In this paper we investigate the mathematical properties of the integrability of the symmetric six-vertex model towards the view of algebraic geometry. We show that the algebraic variety originated from Baxter’s commuting transfer method is birationally isomorphic to a ubiquitous threefold known as Segre cubic primal. This relation makes it possible to present the most generic solution for the Yang–Baxter triple associated to this lattice model. The respective -matrix and Lax operators are parameterized by three independent affine spectral variables.
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