Geodesic
A Simple Proof of Sklyanin's Formula for Canonical Spectral Coordinates of the Rational Calogero–Moser System
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016)

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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.
Keywords: integrable systems; Calogero–Moser type systems; spectral coordinates; Hamiltonian reduction; action-angle duality. 
Tamás F. Görbe. A Simple Proof of Sklyanin's Formula for Canonical Spectral Coordinates of the Rational Calogero–Moser System. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a26/
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