Hidden quantum R-matrix in discrete time classical Heisenberg magnet

Abstract

We construct local M-operators for an integrable discrete time version of the classical Heisenberg magnet by convolution of the twisted quantum trigonometric 4$\times$4 R-matrix with certain vectors in its "quantum" space. Components of the vectors are identified with $τ$-functions of the model. Hirota's bilinear formalism is extensively used. The construction generalizes the known representation of M-operators in continuous time models in terms of Lax operators and classical $r$-matrix.