Action-angle duality between the C(n)-type hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen models

TL;DR

This paper constructs action-angle coordinates for C(n)-type hyperbolic Sutherland and rational Ruijsenaars-Schneider-van Diejen models, establishing a duality between these integrable systems through symplectic reduction.

Contribution

It introduces a dual reduction framework that explicitly demonstrates the action-angle duality for these models, a novel connection in integrable systems theory.

Findings

Explicit action-angle coordinates for both models

Establishment of duality between the models

Framework applicable to C(n) root systems

Abstract

In a symplectic reduction framework we construct action-angle systems of canonical coordinates for both the hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen integrable models associated with the C(n) root system. The presented dual reduction picture permits us to establish the action-angle duality between these many-particle systems.