Beside its usual interpretation as a system of n indistinguishable particles moving on the circle, the trigonometric Sutherland system can be viewed alternatively as a system of distinguishable particles on the circle or on the line, and these three physically distinct systems are in duality with corresponding variants of the rational Ruijsenaars-Schneider system. We explain that the three duality relations, first obtained by Ruijsenaars in 1995, arise naturally from the Kazhdan-Kostant-Sternberg symplectic reductions of the cotangent bundles of the group U(n) and its covering groups U(1)×SU(n) and R×SU(n), respectively. This geometric interpretation enhances our understanding of the duality relations and simplifies Ruijsenaars' original direct arguments that led to their discovery.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics