We establish a connection between a specialization of the nonsymmetric Macdonald 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.
"Nonsymmetric Macdonald polynomials and Demazure characters." Duke Math. J. 116 (2) 299 - 318, 1 February 2003. https://doi.org/10.1215/S0012-7094-03-11624-5