On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system

DOI10.1007/s11005-020-01320-xzbMath1468.70010arXiv1811.08727OpenAlexW3104008428MaRDI QIDQ2224496

Oleg A. Chalykh, Maxime Fairon

Publication date: 3 February 2021

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.08727

zbMATH Keywords

quiversRuijsenaars-Schneider systemquasi-Hamiltonian reductiondouble Poisson brackets

Mathematics Subject Classification ID

Momentum maps; symplectic reduction (53D20) Representations of quivers and partially ordered sets (16G20) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items (12)

Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems ⋮ Hamiltonian structures for integrable nonabelian difference equations ⋮ Poisson-Lie analogues of spin Sutherland models ⋮ Poisson reductions of master integrable systems on doubles of compact Lie groups ⋮ Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and \(R\)-matrix identities ⋮ Integrable multi-Hamiltonian systems from reduction of an extended quasi-Poisson double of \({\mathrm{U}}(n)\) ⋮ Trigonometric real form of the spin RS model of Krichever and Zabrodin ⋮ On the bi-Hamiltonian Structure of the Trigonometric Spin Ruijsenaars–Sutherland Hierarchy ⋮ Superintegrability of Calogero–Moser systems associated with the cyclic quiver ⋮ Superintegrable systems on moduli spaces of flat connections ⋮ Bi-Hamiltonian structure of Sutherland models coupled to two u(n)* -valued spins from Poisson reduction ⋮ Lax equations for relativistic GL(NM,C) Gaudin models on elliptic curve

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Degenerately integrable systems
• Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction
• On the symplectic structure of instanton moduli spaces
• A generalisation of the Calogero-Moser system
• A new class of integrable systems and its relation to solitons
• Action-angle maps and scattering theory for some finite-dimensional integrable systems. I: The pure soliton case
• Collisions of Calogero-Moser particles and an adelic Grassmannian (with an appendix by I. G. Macdonald)
• Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles
• Lie group valued moment maps
• Relativistic Calogero-Moser model as gauged WZW theory.
• \(q\)-KP hierarchy, bispectrality and Calogero-Moser systems
• Noncommutative integrability, moment map and geodesic flows
• Degenerate integrability of the spin Calogero-Moser systems and the duality with the spin Ruijsenaars systems
• The classical \(r\)-matrix for the relativistic Ruijsenaars-Schneider system.
• Why is the Ruijsenaars-Schneider hierarchy governed by the same \(R\)-operator as the Calogero-Moser one?
• Poisson-Lie analogues of spin Sutherland models
• Hyperbolic spin Ruijsenaars-Schneider model from Poisson reduction
• On a family of quivers related to the Gibbons-Hermsen system
• Multiplicative preprojective algebras, middle convolution and the Deligne-Simpson problem
• Multiplicative quiver varieties and generalised Ruijsenaars-Schneider models
• Quantized multiplicative quiver varieties.
• New compact forms of the trigonometric Ruijsenaars-Schneider system
• Poisson involutions, spin Calogero-Moser systems associated with symmetric Lie subalgebras and the symmetric space spin Ruijsenaars-Schneider models
• Double Poisson algebras
• Geometry of Multiplicative Preprojective Algebra
• On the Hamiltonian form of equations of the elliptic spin Ruijsenaars-Schneider model
• Symmetries and integrability
• Elliptic Ruijsenaars - Schneider model via the Poisson reduction of the affine Heisenberg double
• Integrable discretizations of the spin Ruijsenaars–Schneider models
• Quasi-Poisson Manifolds
• On the Hamiltonian structure of the spin Ruijsenaars-Schneider model
• Spin generalization of the Ruijsenaars-Schneider model, the non-Abelian 2D Toda chain, and representations of the Sklyanin algebra
• Spin versions of the complex trigonometric Ruijsenaars–Schneider model from cyclic quivers
• Bi-Hamiltonian structure of a dynamical system introduced by Braden and Hone
• KP hierarchy for the cyclic quiver
• Duality in integrable systems and gauge theories

This page was built for publication: On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system