Low-dimensional tori in Calogero-Moser-Sutherland systems

Abstract

The main result of this paper is an explicit description of the stratification of the phase space of Calogero--Moser--Sutherland (CMS) integrable systems corresponding to Lie groups $SU(n)$. The phase space decomposes into symplectic strata of dimensions $2s$, where $s=0,1,\dots ,n-1$. On each stratum of the positive dimension, we construct natural action-angle coordinates and compute the symplectic form explicitly, showing that every stratum is symplectomorphic to ${\mathbb{R}}_{>0}^s\times {\mathbb{T}}^s$. The zero-dimensional stratum corresponds to the equilibrium point of the multi-time CMS dynamics.