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arXiv · hep-th/9602160

Why are the rational and hyperbolic Ruijsenaars-Schneider hierarchies governed by the same R-operators as the Calogero-Moser ones?

Yuri B. Suris
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Abstract

We demonstrate that in a certain gauge the Lax matrices of the rational and hyperbolic Ruijsenaars--Schneider models have a quadratic $r$-matrix Poisson bracket which is an exact quadratization of the linear $r$--matrix Poisson bracket of the Calogero--Moser models. This phenomenon is explained by a geometric derivation of Lax equations for arbitrary flows of both hierarchies, which turn out to be governed by the same dynamical $R$--operator.

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Yuri B. Suris. 1996-05-20. Why are the rational and hyperbolic Ruijsenaars-Schneider hierarchies governed by the same R-operators as the Calogero-Moser ones?. https://doi.org/10.1016/s0375-9601(96)00897-3

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