INTEGRALS OF MOTION OF THE CLASSICAL LATTICE SINE-GORDON SYSTEM

We compute the local integrals of motions of the classical limit of th e lattice sine-Gordon system, using a geometrical interpretation of th e local sine-Gordon variables. Using an analogous description of the s creened local variables, we show that these integrals are in involutio n. We present some remarks on relations with the situation at the root s of 1 and results on another latticization (linked to the principal s ubalgebra of <(sl)over cap>(2) rather than the homogeneous one). Final ly, we analyze a module of ''screened semilocal variables,'' on which the whole <(sl)over cap>(2) acts.