Generalized model of interacting integrable tops

Abstract

We introduce a family of classical integrable systems describing dynamics of $M$ interacting ${\mathrm{gl}}_N$ integrable tops. It extends the previously known model of interacting elliptic tops. Our construction is based on the ${\mathrm{GL}}_N$ $R$-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 ${\mathrm{gl}}_{NM}$-valued Lax pair with spectral parameter and its classical dynamical $r$-matrix are obtained. Possible applications are briefly discussed.

30 pages, minor changes