Bispectrality of $AG_2$ Calogero-Moser-Sutherland system

TL;DR

This paper investigates the $AG_2$ Calogero-Moser-Sutherland integrable system, establishing bispectrality through the construction of a Baker-Akhiezer function and identifying dual difference operators of Macdonald-Ruijsenaars type.

Contribution

It introduces a Baker-Akhiezer function for the $AG_2$ system and proves its bispectrality, along with explicit dual difference operators, advancing understanding of this integrable model.

Findings

Existence of a Baker-Akhiezer function for the $AG_2$ system

Proof of bispectrality of the system

Explicit form of dual Macdonald-Ruijsenaars operators

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.