The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves

Abstract

We study the elliptic C_n and BC_n Ruijsenaars-Schneider models which is elliptic generalization of system given in hep-th/0006004. The Lax pairs for these models are constructed by Hamiltonian reduction technology. We show that the spectral curves can be parameterized by the involutive integrals of motion for these models. Taking nonrelativistic limit and scaling limit, we verify that they lead to the systems corresponding to Calogero-Moser and Toda types.

arXiv commentLaTeX2e, 25 pages, 1 table, some references added and rearranged together with misprints corrected

References in corpus (33)

• Integrable systems and supersymmetric gauge theory
• Five Dimensional Gauge Theories and Relativistic Integrable Systems
• Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of Sklyanin algebra
• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• Commuting difference operators with polynomial eigenfunctions
• Calogero-Moser Models V: Supersymmetry and Quantum Lax Pair
• Calogero-Moser Models: A New Formulation
• Quantum Calogero-Moser Models: Integrability for all Root Systems
• Seiberg-Witten Curves and Integrable Systems
• Generalised Calogero-Moser models and universal Lax pair operators
• Separation of variables for the Ruijsenaars system
• The Ruijsenaars-Schneider Model in the Context of Seiberg-Witten Theory
• Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras
• Calogero-Moser Models II: Symmetries and Foldings
• Calogero-Moser and Toda Systems for Twisted and Untwisted Affine Lie Algebras
• Towards effective topological gauge theories on spectral curves
• Dynamical r-matrix for the elliptic Ruijsenaars-Schneider system
• 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?
• Calogero-Moser Models III: Elliptic Potentials and Twisting
• Elliptic Ruijsenaars-Schneider model from the cotangent bundle over the two-dimensional current group
• Calogero-Moser Models IV: Limits to Toda theory
• Calogero-Moser systems and Hitchin systems
• Lax Pairs and Spectral Curves for Calogero-Moser and Spin Calogero-Moser Systems
• Integrability of the $C_n$ and $B{C}_n$ Ruijsenaars-Schneider models
• Whitham Deformations of Seiberg-Witten Curves for Classical Gauge Groups
• Commuting difference operators arising from the elliptic C_2^{(1)}-face model
• Double Elliptic Systems: Problems and Perspectives
• Seiberg-Witten theory and duality in integrable systems
• Instanton Correction of Prepotential in Ruijsenaars Model Associated with N=2 SU(2) Seiberg-Witten Theory
• The Lax pair for C_2-type Ruijsenaars-Schneider model
• BC_n Ruijsenaars-Schneider models: R-Matrix structure and hamiltonians
• Theta Functions Associated with the Affine Root Systems and the Elliptic Ruijsenaars Operators

Cited by in corpus (5)

• On factorized Lax pairs for classical many-body integrable systems
• Quantum vs Classical Integrability in Ruijsenaars-Schneider Systems
• Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism
• The Dn Ruijsenaars-Schneider model
• On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system