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Trends Math., 2013, Pages 405–413 (Mi trmat3)  

Lax equations and the Knizhnik–Zamolodchikov connection

O. K. Sheinman

Steklov Mathematical Institute, ul. Gubkina, 8, 119991 Moscow, Russia

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

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Supported in part by the program “Fundamental Problems of Nonlinear Dynamics” of the Russian Academy of Sciences.


DOI: https://doi.org/10.1007/978-3-0348-0448-6_37


Bibliographic databases:

MSC: 17B66, 17B67, 14H10, 14H15, 14H55, 30F30, 81R10, 81T40
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