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

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.

34 pages

References in corpus (4)

• On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models
• Integrable random matrix ensembles
• Spin Calogero models associated with Riemannian symmetric spaces of negative curvature
• On the scattering theory of the classical hyperbolic C(n) Sutherland model

Cited by in corpus (11)

• Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction
• Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models
• The hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars-Schneider-van Diejen models: Lax matrices and duality
• Duality between the trigonometric BC(n) Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system
• Scattering theory of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars--Schneider--van Diejen models
• Lax representation of the hyperbolic van Diejen dynamics with two coupling parameters
• Global description of action-angle duality for a Poisson-Lie deformation of the trigonometric ${\mathrm{BC}}_n$ Sutherland system
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
• On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• Integrable many-body systems of Calogero-Ruijsenaars type
• On the derivation of Darboux form for the action-angle dual of trigonometric BC(n) Sutherland system