Irreducible Characters and Clebsch-Gordan Series for the Exceptional Algebra E6: An Approach through the Quantum Calogero-Sutherland Model

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We re-express the quantum Calogero-Sutherland model for the Lie algebra E6 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.