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Elliptic Solutions to Difference Nonlinear Equations and Nested Bethe Ansatz Equations

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Calogero—Moser— Sutherland Models

Part of the book series: CRM Series in Mathematical Physics ((CRM))

Abstract

We outline an approach to a theory of various generalizations of the elliptic Calogero—Moser (CM) and Ruijsenaars—Schneider (RS) systems based on a special inverse problem for linear operators with elliptic coefficients. Hamiltonian theory of such systems is developed with the help of universal symplectic structure proposed by D. H. Phong and the author. Canonically conjugated variables for spin generalizations of the elliptic CM and RS systems are found.

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Authors
  1. I. Krichever
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Editors and Affiliations

  1. Departamento de Matematicas, Universidad de Chile, Las Palmeras, 3425, Nunoa Santiago, Chile

    Jan Felipe van Diejen

  2. McGill University, James Administration Building, Room 504, Montreal, Quebec, H3A 2T5, Canada

    Luc Vinet

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Krichever, I. (2000). Elliptic Solutions to Difference Nonlinear Equations and Nested Bethe Ansatz Equations. In: van Diejen, J.F., Vinet, L. (eds) Calogero—Moser— Sutherland Models. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1206-5_17

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  • DOI: https://doi.org/10.1007/978-1-4612-1206-5_17

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7043-0

  • Online ISBN: 978-1-4612-1206-5

  • eBook Packages: Springer Book Archive

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