The full phase space of a model in the Calogero-Ruijsenaars family

TL;DR

This paper fully characterizes the phase space of a Calogero-Ruijsenaars model derived from a reduction of a free system on the Heisenberg double, establishing its Liouville integrability across the entire space.

Contribution

It completes the description of the model's full phase space, extending previous work that only covered a dense open subset, and confirms Liouville integrability globally.

Findings

Complete description of the full phase space.

Liouville integrability holds on the entire phase space.

Extension of previous partial analyses.

Abstract

We complete the recent derivation of a Ruijsenaars type system that arises as a reduction of the natural free system on the Heisenberg double of SU(n,n). The previous analysis by Marshall focused on a dense open submanifold of the reduced phase space, and here we describe the full phase space wherein Liouville integrability of the system holds by construction.