# Lax equations and Knizhnik-Zamolodchikov connection

Research paper by Oleg K. Sheinman

Indexed on: 09 Feb '11Published on: 09 Feb '11Published in: Mathematics - Representation Theory

#### 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 action variables then the corresponding operators commute.