The hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars-Schneider-van Diejen models: Lax matrices and duality

TL;DR

This paper constructs action-angle variables for hyperbolic BC(n) Sutherland and rational BC(n) Ruijsenaars-Schneider-van Diejen models, establishing their duality through symplectic reduction and Lax matrix construction.

Contribution

It introduces a symplectic reduction approach to derive action-angle variables and duality for these integrable models, including a new Lax matrix construction.

Findings

Established action-angle duality between the models

Constructed explicit Lax matrix for the BC(n) rational model

Provided a symplectic reduction framework for these systems

Abstract

In this paper, we construct canonical action-angle variables for both the hyperbolic BC(n) Sutherland and the rational BC(n) 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 BC(n)-type rational Ruijsennars-Schneider-van Diejen model.