Rational Calogero-Moser Model: Explicit Form and r-Matrix of the Second Poisson Structure

被引：5

作者：

Avan, Jean ^{[1
]}

Ragoucy, Eric ^{[2
,3
]}

机构：

[1] Univ Cergy Pontoise, CNRS, Lab Phys Theor & Modelisat, UMR 8089, F-95302 Cergy Pontoise, France

[2] CNRS, LAPTH Annecy le Vieux, F-74941 Annecy Le Vieux, France

[3] Univ Savoie, F-74941 Annecy Le Vieux, France

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2012年 / 8卷

关键词：

classical integrable systems; hierarchy of Poisson structures; dynamical reflection equation; SYSTEMS; EQUATION;

D O I：

10.3842/SIGMA.2012.079

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We compute the full expression of the second Poisson bracket structure for N = 2 and N = 3 site rational classical Calogero-Moser model. We propose an r-matrix formulation for N = 2. It is identified with the classical limit of the second dynamical boundary algebra previously built by the authors.

引用

页数：13

共 32 条

[1] Poisson structures of Calogero-Moser and Ruijs']jsenaars-Schneider models
Aniceto, Ines
Avan, Jean
Jevicki, Antal
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (18)
[2] [Anonymous], 2003, CAMBRIDGE MONOGRAPHS
[3] R-matrix quantization of the elliptic Ruijs']jsenaars-Schneider model
Arutyunov, GE
Chekhov, LO
Frolov, SA
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1998, 192 (02) : 405 - 432
[4] Quantum dynamical R-matrices and quantum Frobenius group
Arutyunov, GE
Frolov, SA
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1998, 191 (01) : 15 - 29
[5] CLASSICAL R-MATRIX STRUCTURE FOR THE CALOGERO MODEL
AVAN, J
TALON, M
[J]. PHYSICS LETTERS B, 1993, 303 (1-2) : 33 - 37
[6] Avan J., 1994, ST PETERSB MATH J, V6, P255
[7] Classification of Non-Affine Non-Hecke Dynamical R-Matrices
Avan, Jean
Billaud, Baptiste
Rollet, Genevieve
[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2012, 8
[8] A New Dynamical Reflection Algebra and Related Quantum Integrable Systems
Avan, Jean
Ragoucy, Eric
[J]. LETTERS IN MATHEMATICAL PHYSICS, 2012, 101 (01) : 85 - 101
[9] HAMILTONIAN STRUCTURES AND LAX EQUATIONS
BABELON, O
VIALLET, CM
[J]. PHYSICS LETTERS B, 1990, 237 (3-4) : 411 - 416
[10] CLASSICAL R-MATRIX AND EXCHANGE ALGEBRA IN WZNW AND TODA THEORIES
BALOG, J
DABROWSKI, L
FEHER, L
[J]. PHYSICS LETTERS B, 1990, 244 (02) : 227 - 234

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