A procedure is described that makes use of the generating function of characters to obtain a new generating function $H$ giving the multiplicities of each weight in all the representations of a simple Lie algebra. The way to extract from $H$ explicit
multiplicity formulas for particular weights is explained and the results corresponding to rank two simple Lie algebras shown.
We solve perturbatively the quantum elliptic Calogero-Sutherland model in the regime in which the quotient between the real and imaginary semiperiods of the Weierstrass ${cal P}$ function is small
