  We give an expression of the $q$-analogues of the multiplicities of weights
in irreducible $\sl_{n+1}$-modules in terms of the geometry of the crystal
graph attached to the corresponding $U_q(\sl_{n+1})$-modules. As an
application, we describe multivariate polynomial analogues of the
multiplicities of the zero weight, refining Kostant's generalized exponents.
