Bispectrality of $A{G}_2$ Calogero-Moser-Sutherland system

Abstract

We consider the generalised Calogero-Moser-Sutherland quantum integrable system associated to the configuration of vectors $A{G}_2$, 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.

25 pages

References in corpus (3)

• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Intertwining operator for $A{G}_2$ Calogero-Moser-Sutherland system
• Wave function for $GL(n,\mathbb{R})$ hyperbolic Sutherland model II. Dual Hamiltonians

Cited by in corpus (1)

• Baker-Akhiezer function for the deformed root system $BC(l,1)$ and bispectrality