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

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arxiv math/0202245 v1 pith:2UVJC55O submitted 2002-02-23 math.QA math.SG

N.Reshetikhin This is my paper · ORCID
classification math.QAmath.SG
keywords spinsystemscalogero-moserdegeneratedimensionintegrabilityintegrableruijsenaars
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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.

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Cited by 1 Pith paper

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  1. Integrable systems from Poisson reductions of generalized Hamiltonian torus actions

    math-ph 2025-07 unverdicted novelty 7.0 of 10

    Develops sufficient conditions for Poisson reduction of generalized Hamiltonian torus actions to preserve integrability and applies them to open problems on Lie group doubles and flat-connection moduli spaces.

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