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A model of the non-Abelian fractional quantum Hall effect is obtained fromthe diagonalization of the matrix model proposed by Dorey, Tong, and Turner(DTT). The Hamiltonian is reminiscent of a spin Calogero-Moser model butinvolves higher-order symmetric representations of the non-Abelian symmetry. Wederive the energy spectrum and show that the Hamiltonian has a triangularaction on a certain class of wave functions with a free fermion expression. Wededuce the expression of the ground states eigenfunctions and show that theysolve a Knizhnik-Zamolodchikov equation. Finally, we discuss the emergence ofKac-Moody symmetries in the large $N$ limit using the level-rank duality andconfirm the results obtained previously by DTT.

A Calogero model for the non-Abelian quantum Hall effect