arXiv:solv-int/9603006 · Journal of Physics A Mathematical and General

Dynamicalr-matrix for the elliptic Ruijsenaars - Schneider system

Frank Willem Nijhoff, V B Kuznetsov, E K Sklyanin, O Ragnisco

Published Jul 7, 1996• 36 citations

Abstract

The classical r -matrix structure for the generic elliptic Ruijsenaars - Schneider model is presented. It makes manifest the integrability of this model as well as of its discrete-time version that was constructed in a recent paper.

DOI: 10.1088/0305-4470/29/13/005

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arXiv:solv-int/9603006 · Journal of Physics A Mathematical and General

Dynamicalr-matrix for the elliptic Ruijsenaars - Schneider system

Frank Willem Nijhoff, V B Kuznetsov, E K Sklyanin, O Ragnisco

Published Jul 7, 1996• 36 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/0305-4470/29/13/005

Related papers

Classical r -matrix structure for elliptic Ruijsenaars chain and 1 + 1 field analogue of Ruijsenaars–Schneider model

Dmitrii Murinov, Andrei Vladimirovich Zotov

arXiv:2508.12656Journal of Physics A Mathematical and TheoreticalDec 8, 20252 citations

The Nondynamical r -Matrix Structure of the Elliptic Ruijsenaars–Schneider Model with N = 2

Hou BoYu, Wen‐Li Yang

Communications in Theoretical PhysicsApr 30, 20000 citations

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

Bo-Yu Hou, Wen‐Li Yang

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Jean Avan, G. Rollet

This paper is replaced and superseded by nlin.SI/0106015 (Title: Structures in BC_N Ruijsenaars-Schneider models)

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On the $R$ -matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operatorsOn the $$R$$-matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operators

Mariya Georgievna Matushko, Andrei Vladimirovich Zotov

We propose and prove a set of identities for the elliptic $GL_M$ $R$ -matrix (in the fundamental representation). In the scalar case ( $M=1$ ), these are elliptic function identities derived by Ruijsenaars as necessary and sufficient conditions for his kernel identity underlying the construction of integral solutions of quantum spinless Ruijsenaars–Schneider model. In this respect, our result can be regarded as a first step toward constructing solutions of the quantum eigenvalue problem for the anisotropic spin Ruijsenaars model.We propose and prove a set of identities for the elliptic $$GL_M$$ $$R$$ -matrix (in the fundamental representation). In the scalar case ( $$M=1$$ ), these are elliptic function identities derived by Ruijsenaars as necessary and sufficient conditions for his kernel identity underlying the construction of integral solutions of quantum spinless Ruijsenaars–Schneider model. In this respect, our result can be regarded as a first step toward constructing solutions of the quantum eigenvalue problem for the anisotropic spin Ruijsenaars model.

arXiv:2211.08529Theoretical and Mathematical PhysicsNov 1, 20221 citation

On the

R

-matrix identities related to elliptic anisotropic spin Ruijsenaars–Macdonald operators

We propose and prove a set of identities for the elliptic

GL_M

R

-matrix (in the fundamental representation). In the scalar case (

M=1

), these are elliptic function identities derived by Ruijsenaars as necessary and sufficient conditions for his kernel identity underlying the construction of integral solutions of quantum spinless Ruijsenaars–Schneider model. In this respect, our result can be regarded as a first step toward constructing solutions of the quantum eigenvalue problem for the anisotropic spin Ruijsenaars model.