Exact Yangian Symmetry in the Classical Euler-Calogero-Moser Model

Abstract

We compute the $r$-matrix for the elliptic Euler-Calogero-Moser model. In the trigonometric limit we show that the model possesses an exact Yangian symmetry.

10 pages, Latex, par-lpthe 94-03

References in corpus (2)

• Yang-Baxter equation in spin chains with long range interactions
• Integrable Systems for Particles with Internal Degrees of Freedom

Cited by in corpus (23)

• Introduction to Yangian symmetry in integrable field theory
• Integrable spin Calogero-Moser systems
• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• Collective field theory of the matrix-vector model
• Elliptic Ruijsenaars-Schneider and Calogero-Moser hierarchies are governed by the same r-matrix
• Why are the rational and hyperbolic Ruijsenaars-Schneider hierarchies governed by the same R-operators as the Calogero-Moser ones?
• Spin Calogero-Moser systems associated with simple Lie algebras
• Notes on Collective Field Theory of Matrix and Spin Calogero Models
• W-superalgebras as truncation of super-Yangians
• Generalized model of interacting integrable tops
• On Hamiltonian structure of the spin Ruijsenaars-Schneider model
• On R-matrix valued Lax pairs for Calogero-Moser models
• Elliptic Ruijsenaars-Schneider model via the Poisson reduction of the Affine Heisenberg Double
• The Classical $r$-Matrix for the Relativistic Ruijsenaars-Schneider System
• Yangian-invariant field theory of matrix-vector models
• Observable algebra for the rational and trigonometric Euler Calogero Moser models
• Quasi-compact Higgs bundles and Calogero-Sutherland systems with two types spins
• Integrable discretizations of the spin Ruijsenaars-Schneider models
• Relativistic interacting integrable elliptic tops
• The symplectic structure of the spin Calogero model
• Calogero-Sutherland system with two types interacting spins
• Liouville integrability of a class of integrable spin Calogero-Moser systems and exponents of simple Lie algebras
• Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates