Degenerate Integrability of Spin Calogero-Moser Systems and the duality with the spin Ruijsenaars systems

Abstract

It is shown that spin Calogero-Moser systems are completely integrable in a sense of degenerate integrability. Their Liouville tori have dimension less then half of the dimension of the phase space. It is also shown that rational spin Ruijsenaars systems are degenerately integrable and dual to spin Calogero- Moser systems in a sense that action-algle variables of one are angle-action variables of the other.

References in corpus (2)

• Spin Calogero-Moser systems associated with simple Lie algebras
• Automorphisms and Ideals of the Weyl Algebra

Cited by in corpus (10)

• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• Integrable systems from the classical reflection equation
• Poisson-Lie analogues of spin Sutherland models
• Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers
• Morphisms of double (quasi-)Poisson algebras and action-angle duality of integrable systems
• Superintegrability of Calogero-Moser systems associated with the cyclic quiver
• Bi-Hamiltonian structure of spin Sutherland models: the holomorphic case
• The Ruijsenaars self-duality map as a mapping class symplectomorphism
• Generalized spin Sutherland systems revisited
• Integrable systems on multiplicative quiver varieties from cyclic quivers