On R-matrix valued Lax pairs for Calogero-Moser models

This article is devoted to the study of R-matrix-valued Lax pairs for N-body (elliptic) Calogero-Moser models. Their matrix elements are given by quantum R-matrices of Baxter-Belavin type. For the widely known Krichever's Lax pair with spectral parameter is reproduced. First, we construct the R...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2018-08, Vol.51 (31), p.315202
Main Authors: Grekov, A, Zotov, A
Format: Article
Language:English
Subjects:
Calogero-Moser models
elliptic integrable systems
Lax pairs
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Summary:This article is devoted to the study of R-matrix-valued Lax pairs for N-body (elliptic) Calogero-Moser models. Their matrix elements are given by quantum R-matrices of Baxter-Belavin type. For the widely known Krichever's Lax pair with spectral parameter is reproduced. First, we construct the R-matrix-valued Lax pairs for Calogero-Moser models associated with classical root systems. For this purpose we study generalizations of the D'Hoker-Phong Lax pairs. It appeared that in the R-matrix-valued case the Lax pairs exist in special cases only. The number of quantum spaces (on which R-matrices act) and their dimension depend on the values of coupling constants. Some of the obtained classical Lax pairs admit straightforward extension to the quantum case. In the end we describe a relationship of the R-matrix-valued Lax pairs to Hitchin systems defined on bundles with nontrivial characteristic classes over elliptic curve. We show that the classical analogue of the anisotropic spin exchange operator entering the R-matrix-valued Lax equations is reproduced in these models.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/aac7b6