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

SIGMA 12 (2016), 027, 5 pages      arXiv:1601.01181      https://doi.org/10.3842/SIGMA.2016.027

### A Simple Proof of Sklyanin's Formula for Canonical Spectral Coordinates of the Rational Calogero-Moser System

Tamás F. Görbe
Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, H-6720 Szeged, Hungary

Received January 19, 2016, in final form March 08, 2016; Published online March 11, 2016

Abstract
We use Hamiltonian reduction to simplify Falqui and Mencattini's recent proof of Sklyanin's expression providing spectral Darboux coordinates of the rational Calogero-Moser system. This viewpoint enables us to verify a conjecture of Falqui and Mencattini, and to obtain Sklyanin's formula as a corollary.

Key words: integrable systems; Calogero-Moser type systems; spectral coordinates; Hamiltonian reduction; action-angle duality.

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