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Lax Equations and the Knizhnik–Zamolodchikov Connection

  • Oleg K. SheinmanEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)

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 commutingH amiltonians of the Lax system projectively commute. If Hamiltonians depend only on the action variables then the correspondingop erators commute

Keywords

Current algebra Lax operator algebra Lax integrable system Knizhnik-Zamolodchikov connection 

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© Springer Basel 2013

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia

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