Calogero–Moser Model and R-Matrix Identities

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...

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Bibliographic Details
Published in:Theoretical and mathematical physics 2018-12, Vol.197 (3), p.1755-1770
Main Author: Zotov, A. V.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Elliptic functions
Hamiltonian functions
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary: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.
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577918120061