Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Classical r-matrices for the Elliptic Calogero Model in Harmonic Potential

Shyang-Ling Lou, Yih-Shyan Su

Published Jul 1, 2013• 0 citations
OpenAlex

Abstract

For the classical elliptic Calogero system in an external harmonic potential it is shown that the Lax operator L+L − possesses a classical r-matrix structure. The relation of the r-matrix and the Yang-Baxter equation involving another dynamical matrix are discussed.

Related papers

The non-dynamicalr-matrix structure for the elliptic Calogero-Moser model

Bo-Yu Hou, Wen‐Li Yang

In this paper we construct a new Lax operator for the elliptic Calogero-Moser model with general from the classical dynamical twisting, in which the corresponding r -matrix is purely numerical (non-dynamic). The non-dynamical r -matrix structure of this Lax operator is obtained, which is the elliptic -symmetric r -matrix.

Journal of Physics A Mathematical and General•Jan 1, 1999•11 citations

The nondynamical r-matrix structure of the elliptic Ruijsenaars-Schneider model with N=2

Bo-Yu Hou, Wen‐Li Yang

We demonstrate that in a certain gauge the elliptic Ruijsenaars-Shneider model with N=2 admits a nondynamical r-matrix structure and the corresponding classical r-matrix is the same as that of its non-relativistic counterpart (Calogero-Moser model) in the same gauge.The relation between our (classical)Lax operator and the Lax operator given by Ruijsenaars is also obtained.

arXiv:solv-int/9802015•Feb 22, 1998•0 citations

Non-ultralocal classical r-matrix structure for 1+1 field analogue of elliptic Calogero–Moser model

Andrei Vladimirovich Zotov

Abstract We consider 1+1 field generalization of the elliptic Calogero–Moser model. It is shown that the Lax connection satisfies the classical non-ultralocal r-matrix structure of Maillet type. Next, we consider 1+1 field analogue of the spin Calogero–Moser model and its multipole (or multispin) extension. Finally, we discuss the field analogue of the classical IRF-Vertex correspondence, which relates utralocal and non-ultralocal r-matrix structures.

arXiv:2404.01898•Journal of Physics A Mathematical and Theoretical•Jul 3, 2024•7 citations

R-matrix valued Lax pair for elliptic Calogero–Inozemtsev system and associative Yang–Baxter equations of $$\textrm{BC}_n$$ type

Mariya Georgievna Matushko, A. Mostovskii, Andrei Vladimirovich Zotov

arXiv:2503.22659•Letters in Mathematical Physics•Jan 17, 2026•1 citation

$R$-matrices for the $n=2,3$ Elliptic Calogero-Moser Models

Braden, H W, Suzuki, T

The classical (dynamical) $R$-matrices for the 2- and 3-body Calogero-Moser models with elliptic potentials are given. The 3-body case has an interesting nontrivial structure that goes beyond the known ansatz for momentum independent $R$-matrices. The $R$-matrices presented include the dynamical $R$-matrices of Avan and Talon as degenerate cases of the elliptic potential.

•Dec 3, 1993•6 citations

Classical R-matrix structure for the Calogero model

M.Talon ∗ A classical R-matrix structure is described for the Lax representation of the integrable n-particle chains of Calogero-Olshanetski-Perelomov. This R-matrix is dynamical, non antisymmetric and non-invertible. It immediately triggers the integrability of the Type I, II and III potentials, and the algebraic structures associated with the Type V potential. PAR LPTHE 92/40 Work sponsored by CNRS, France.

•Jan 1, 1992•0 citations
R-matrix valued Lax pair for elliptic Calogero–Inozemtsev system and associative Yang–Baxter equations of BCn\textrm{BC}_nBCn​ type
RRR-matrices for the n=2,3n=2,3n=2,3 Elliptic Calogero-Moser Models
The classical (dynamical) RRR-matrices for the 2- and 3-body Calogero-Moser models with elliptic potentials are given. The 3-body case has an interesting nontrivial structure that goes beyond the known ansatz for momentum independent RRR-matrices. The RRR-matrices presented include the dynamical RRR-matrices of Avan and Talon as degenerate cases of the elliptic potential.