Generalized model of interacting integrable tops

• Main Authors: A. Grekov, I. Sechin, A. Zotov
• Format: Article
• Language: English
• Published: SpringerOpen 2019-10-01
• Series: Journal of High Energy Physics
• Subjects: Lattice Integrable Models; Matrix Models; Differential and Algebraic Geometry
• Online Access: http://link.springer.com/article/10.1007/JHEP10(2019)081

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