Abstract
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.
Highlights
We introduce a family of classical integrable systems describing dynamics of M interacting glN integrable tops
We deal with the models admitting the Lax pairs with spectral parameter on elliptic curves [61, 62]
A possible application of the obtained family of integrable models is in constructing quantum integrable anisotropic long-rang spin chains
Summary
We construct the N M × N M Lax pair L(z), M(z) satisfying the Lax equations. Our construction is based on GLN R-matrix — solution of the associative Yang-Baxter equation (1.8). Besides (1.8) the R-matrix should satisfy a set of properties
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