Lax equations and the Knizhnik–Zamolodchikov connection

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 commutingHamiltonians of the Lax system projectively commute. If Hamiltonians depend only on the action variables then the corresponding operators commute.