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Theoretical and Mathematical Physics

, Volume 197, Issue 3, pp 1755–1770 | Cite as

Calogero–Moser Model and R-Matrix Identities

  • A. V. ZotovEmail author
Article
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Abstract

We discuss properties of R-matrix-valued Lax pairs for the elliptic Calogero-Moser model. In particular, we show that the family of Hamiltonians arising from this Lax representation contains only known Hamiltonians and no others. We review the relation of R-matrix-valued Lax pairs to Hitchin systems on bundles with nontrivial characteristic classes over elliptic curves and also to quantum long-range spin chains. We prove a general higher-order identity for solutions of the associative Yang–Baxter equation.

Keywords

elliptic integrable system long-range spin chain associative Yang–Baxter equation 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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