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We re-express the quantum Calogero-Sutherland model for the Lie algebra $E_6$and the particular value of the coupling constant $\kappa=1$ by using thefundamental irreducible characters of the algebra as dynamical variables. Forthat, we need to develop a systematic procedure to obtain all theClebsch-Gordan series required to perform the change of variables. We describehow the resulting quantum Hamiltonian operator can be used to compute morecharacters and Clebsch-Gordan series for this exceptional algebra.Comment: 22 pages, 1 figur

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