A dynamical system connected with inhomogeneous $6$-vertex model

A completely integrable dynamical system in discrete time is studied by means of algebraic geometry. The system is associated with factorization of a linear operator acting in a direct sum of three linear spaces into a product of three operators, each acting nontrivially only in a direct sum of two spaces, and the following reversing of the order of factors. There exists a reduction of the system interpreted as a classical field theory in $2+1$-dimensional space-time, the integrals of motion coinciding, 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). Thus, a connection with the “local”, or “generalized”, quantum Yang–Baxter equation is revealed. Bibliography: 10 titles.