Intertwining operator for $A{G}_2$ Calogero-Moser-Sutherland system

Abstract

We consider generalised Calogero-Moser-Sutherland quantum Hamiltonian $H$ associated with a configuration of vectors $A{G}_2$ on the plane which is a union of $A_2$ and $G_2$ root systems. The Hamiltonian $H$ depends on one parameter. We find an intertwining operator between $H$ and the Calogero-Moser-Sutherland Hamiltonian for the root system $G_2$. This gives a quantum integral for $H$ of order 6 in an explicit form thus establishing integrability of $H$.

24 pages

References in corpus (1)

• Trigonometric Solutions of WDVV Equations and Generalized Calogero-Moser-Sutherland Systems