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Generalized model of interacting integrable tops

Journal of High Energy Physics. 2019. Vol. 10. No. 081. P. 1–32.
Grekov A., Sechin I., Zotov A.

We introduce a family of classical integrable systems describing dynamics of M interacting glN integrable tops. It extends the previously known model of interacting elliptic tops. Our construction is based on the GLNR-matrix satisfying the associative Yang-Baxter equation. The obtained systems can be considered as extensions of the spin type Calogero-Moser models with (the classical analogues of) anisotropic spin exchange operators given in terms of the R-matrix data. In N = 1 case the spin Calogero-Moser model is reproduced. Explicit expressions for glNM -valued Lax pair with spectral parameter and its classical dynamical r-matrix are obtained. Possible applications are briefly discussed.

Research target: Physics Mathematics
Language: English
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Keywords: Matrix ModelsLattice Integrable ModelsDifferential and Algebraic Geometry
Publication based on the results of:
Development of combinatorial, homological and geometric methods in the theory of moduli spaces of algebraic curves and their mappings, with applications to problems of mathematical physics (2019)
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