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.