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

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.

26 pages

References in corpus (2)

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

Cited by in corpus (23)

• Quantum Lax pairs via Dunkl and Cherednik operators
• New compact forms of the trigonometric Ruijsenaars-Schneider system
• The action-angle dual of an integrable Hamiltonian system of Ruijsenaars--Schneider--van Diejen type
• Duality between the trigonometric BC(n) Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system
• Difference equation for the Heckman-Opdam hypergeometric function and its confluent Whittaker limit
• Lax representation of the hyperbolic van Diejen dynamics with two coupling parameters
• Scattering theory of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars--Schneider--van Diejen models
• The full phase space of a model in the Calogero-Ruijsenaars family
• Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems
• Global description of action-angle duality for a Poisson-Lie deformation of the trigonometric ${\mathrm{BC}}_n$ Sutherland system
• On a Poisson-Lie deformation of the 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)
• The Ruijsenaars self-duality map as a mapping class symplectomorphism
• Integrable multi-Hamiltonian systems from reduction of an extended quasi-Poisson double of $U(n)$
• On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• On the r-matrix structure of the hyperbolic BC(n) Sutherland model
• Classical elliptic ${\mathrm{BC}}_1$ Ruijsenaars-van Diejen model: relation to Zhukovsky-Volterra gyrostat and 1-site classical XYZ model with boundaries
• Equivalence of two sets of Hamiltonians associated with the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• Integrable many-body systems of Calogero-Ruijsenaars type
• Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions
• Stable equilibria for the roots of the symmetric continuous Hahn and Wilson polynomials
• Lax matrices for a 1-parameter subfamily of van Diejen--Toda chains
• On the derivation of Darboux form for the action-angle dual of trigonometric BC(n) Sutherland system