Quantisation of compact forms of the trigonometric Ruijsenaars-Schneider system
(Chalmers University of Technology)
Recently, new forms of the compactified trigonometric Ruijsenaars-Schneider model have been discovered at the level of classical mechanics by Fehér and Kluck. These models describe N particles moving on a circle whose completed center-of-mass phase space is the complex projective space CPN−1 with the Fubini-Study form. In this talk, we present the quantum version of these integrable systems and solve the corresponding eigenvalue problem by generalising earlier results by van Diejen and Vinet.