Irreducible characters and Clebsch-Gordan series for the exceptional algebra $E_6$: an approach through the quantum Calogero-Sutherland model

We re-express the quantum Calogero-Sutherland model for the Lie algebra $E_6$ and the particular value of the coupling constant $κ=1$ by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan series required to perform the change of variables. We describe how the resulting quantum Hamiltonian operator can be used to compute more characters and Clebsch-Gordan series for this exceptional algebra.

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