Nonsymmetric Macdonald polynomials and Demazure characters

We establish a connection between a specialization of thenonsymmetric Mocdonald polynomials and the Demazure characters of the corresponding affine Kac-Moody algebra. This allows us to obtain a representation-theoretical interpretation of the coefficients of the expansion of the specialized symmetric Macdonald polynomials in the basis formed by the irreducible characters of the associated finite Lie algebra.