Geodesic
Calogero--Moser model and $R$-matrix identities
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 3, pp. 417-434

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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. 
@article{TMF_2018_197_3_a5,
     author = {A. V. Zotov},
     title = {Calogero--Moser model and $R$-matrix identities},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {417--434},
     publisher = {mathdoc},
     volume = {197},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a5/}
}
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A. V. Zotov. Calogero--Moser model and $R$-matrix identities. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 3, pp. 417-434. http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a5/