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We consider generalised Calogero-Moser-Sutherland quantum Hamiltonian $H$associated with a configuration of vectors $AG_2$ on the plane which is a unionof $A_2$ and $G_2$ root systems. The Hamiltonian $H$ depends on one parameter.We find an intertwining operator between $H$ and the Calogero-Moser-SutherlandHamiltonian for the root system $G_2$. This gives a quantum integral for $H$ oforder 6 in an explicit form thus establishing integrability of $H$.

Intertwining operator for $AG_2$ Calogero-Moser-Sutherland system