Bispectrality of AG_2 Calogero–Moser–Sutherland System

Abstract

We consider the generalised Calogero–Moser–Sutherland quantum integrable system associated to the configuration of vectors AG_2, which is a union of the root systems A_2 and G_2. We establish the existence of and construct a suitably defined Baker–Akhiezer function for the system, and we show that it satisfies bispectrality. We also find two corresponding dual difference operators of rational Macdonald–Ruijsenaars type in an explicit form.