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 $\kappa=1$ 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. 
J. Fernandez-Nunez, W. Garcia-Fuertes, A. M. Perelomov