Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 079, 13 pages      arXiv:1207.5368      https://doi.org/10.3842/SIGMA.2012.079

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

Jean Avan a and Eric Ragoucy b
a) Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise (CNRS UMR 8089), Saint-Martin 2, 2, av. Adolphe Chauvin, F-95302 Cergy-Pontoise Cedex, France
b) LAPTH Annecy le Vieux, CNRS and Université de Savoie, 9 chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux Cedex, France

Received July 24, 2012, in final form October 17, 2012; Published online October 26, 2012

Abstract
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.

Key words: classical integrable systems; hierarchy of Poisson structures; dynamical reflection equation.

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