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TMF, 2018, Volume 197, Number 3, Pages 417–434 (Mi tmf9625)  

Calogero–Moser model and $R$-matrix identities

A. V. Zotov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

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.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This research is supported by a grant from the Russian Science Foundation (Project No. 14-50-00005).


DOI: https://doi.org/10.4213/tmf9625

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English version:
Theoretical and Mathematical Physics, 2018, 197:3, 1755–1770

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Received: 04.09.2018

Citation: A. V. Zotov, “Calogero–Moser model and $R$-matrix identities”, TMF, 197:3 (2018), 417–434; Theoret. and Math. Phys., 197:3 (2018), 1755–1770

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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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