A dynamical system connected with an inhomogeneous 6-vertex model

Abstract

A completely integrable dynamical system in discrete time is studied by methods of algebraic geometry. The system is associated with factorization of a linear operator acting in the direct sum of three linear spaces into a product of three operators, each acting nontrivially only in the direct sum of two spaces, and subsequently reversing the order of the factors. There exists a reduction of the system, which can be interpreted as a classical field theory in the 2+1-dimensional space-time, whose integrals of motion coincide, in essence, with the statistical sum of an inhomogeneous 6-vertex free-fermion model on the 2-dimensional kagome lattice (here the statistical sum is a function of two parameters). This establishes a connection with the “local,” or “generalized,” quantum Yang-Baxter equation. Bibliography:10 titles.