  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.
