The hyperbolic BCn Sutherland and the rational BCn Ruijsenaars-Schneider-van Diejen models: Lax matrices and duality

In this paper, we construct canonical action-angle variables for both the hyperbolic BCn Sutherland and the rational BCn Ruijsenaars-Schneider-van Diejen models with three independent coupling constants. As a byproduct of our symplectic reduction approach, we establish the action-angle duality between these many-particle systems. The presented dual reduction picture builds upon the construction of a Lax matrix for the BCn-type rational Ruijsenaars-Schneider-van Diejen model.