CRYSTAL GRAPHS AND Q-ANALOGS OF WEIGHT MULTIPLICITIES FOR THE ROOT-SYSTEM A(N)

Abstract : 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 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.