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We express the Hamiltonian of the quantum trigonometric Calogero-Sutherlandmodel for the Lie algebra E8 and coupling constant k=1 by using the fundamentalirreducible characters of the algebra as dynamical independent variables. Then,we compute the second order characters of the algebra and some higher ordercharacters.

Quantum trigonometric Calogero-Sutherland model and irreducible characters for the exceptional algebra E8