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arXiv · 1901.02082

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

Misha Feigin·Martin Vrabec
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Abstract

We consider generalised Calogero-Moser-Sutherland quantum Hamiltonian $H$ associated with a configuration of vectors $AG_2$ 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 $H$.

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Misha Feigin, Martin Vrabec. 2019-01-07. Intertwining operator for $AG_2$ Calogero-Moser-Sutherland system. https://doi.org/10.1063/1.5090274

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