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

2016, March 11
Tamás F. Görbe
Symmetry, Integrability and Geometry: Methods and Applications
  sigma16-027.pdf

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.