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Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of Sklyanin algebra

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arxiv hep-th/9505039 v1 pith:YZDSJ4KQ submitted 1995-05-07 hep-th

I.Krichever , A.Zabrodin This is my paper · ORCID
classification hep-th
keywords algebrarepresentationssklyaninchainellipticequationsnon-abelianoperators
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Action-angle type variables for spin generalizations of the elliptic Ruijsenaars-Schneider system are constructed. The equations of motion of these systems are solved in terms of Riemann theta-functions. It is proved that these systems are isomorphic to special elliptic solutions of the non-abelian 2D Toda chain. A connection between the finite gap solutions of solitonic equations and representations of the Sklyanin algebra is revealed and discrete analogs of the Lame operators are introduced. A simple way to construct representations of the Sklyanin algebra by difference operators is suggested.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Spin Ruijsenaars-Schneider models are Coulomb branches

    hep-th 2026-03 conditional novelty 7.0 of 10

    Cohomological and K-theoretic Coulomb branches of necklace quivers are shown to provide the Poisson structures and Hamiltonians that generate the rational and hyperbolic spin Ruijsenaars–Schneider equations of motion.

  2. Compatible Poisson structures on multiplicative quiver varieties

    math.SG 2023-10 unverdicted novelty 7.0 of 10

    Multiplicative quiver varieties carry a pencil of dimension ℓ(ℓ-1)/2 of compatible Poisson structures obtained by reduction from a pencil of Hamiltonian quasi-Poisson structures.

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