Lax equations and Knizhnik-Zamolodchikov connection

Details Lax equations and Knizhnik-Zamolodchikov connection Lax equations and Knizhnik-Zamolodchikov connection

2010-09-23

arxiv.org/abs/1009.4706v2

Mathematics

Representation Theory

21 pages. Corrected misprints. Some arguments revised, results unchanged

Scientific paper

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.

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