Spectra of the quantized action variables of the compactified Ruijsenaars–Schneider system

We present a simple derivation of the spectra of the action variables of the quantized compactified Ruijsenaars–Schneider system. We obtain the spectra by combining Kähler quantization with the identification of the classical action variables as a standard toric moment map on a complex projective space. The result is consistent with the Schrödinger quantization of the system previously developed by van Diejen and Vinet.