Lax equations and the Knizhnik-Zamolodchikov connection

Abstract

Given a Lax system of equations with the spectral parameter on a Riemann surface we construct a projective unitary representation of the Lie algebra of Hamiltonian vector fields by Knizhnik-Zamolodchikov operators. This provides a prequantization of the Lax system. The representation operators of Poisson commuting Hamiltonians of the Lax system projectively commute. If Hamiltonians depend only on the action variables then the correspondingop erators commute.