The action-angle dual of an integrable Hamiltonian system of Ruijsenaars--Schneider--van Diejen type

Abstract

Integrable deformations of the hyperbolic and trigonometric ${\mathrm{BC}}_n$ Sutherland models were recently derived via Hamiltonian reduction of certain free systems on the Heisenberg doubles of $\mathrm{SU}(n,n)$ and $\mathrm{SU}(2n)$, respectively. As a step towards constructing action-angle variables for these models, we here apply the same reduction to a different free system on the double of $\mathrm{SU}(2n)$ and thereby obtain a novel integrable many-body model of Ruijsenaars--Schneider--van Diejen type that is in action-angle duality with the respective deformed Sutherland model.

21 pages, v2: typos removed, references updated

References in corpus (3)

• Physics and Mathematics of Calogero particles
• Duality between the trigonometric BC(n) Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system
• The full phase space of a model in the Calogero-Ruijsenaars family

Cited by in corpus (11)

• Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models
• On factorized Lax pairs for classical many-body integrable systems
• Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers
• Characteristic determinant and Manakov triple for the double elliptic integrable system
• Global description of action-angle duality for a Poisson-Lie deformation of the trigonometric ${\mathrm{BC}}_n$ Sutherland system
• Quantum-classical duality for Gaudin magnets with boundary
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
• Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
• Integrable many-body systems of Calogero-Ruijsenaars type
• Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish