Abstract
We demonstrate that in a certain gauge the Lax matrix of the Ruijsenaars-Schneider (RS) model has a quadratic r-matrix structure independent of the relativistic parameter of the model. In particular, the dynamical r-matrix object governing the hierarchy of Lax equations connected with the RS model, turns out to be identical with the r-matrix of the Calogero-Moser (CM) model. In the degenerate cases (hyperbolic and rational) this phenomenon is partly explained by a geometric derivation of Lax equations for arbitrary flows of both the RS and the CM hierarchies.
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