On Demazure polynomials

The dimension of the Demazure module, Ew(λ), for an affine Kac–Moody algebra, is a polynomial in λ, called a Demazure polynomial. In this article, we prove that it is harmonic. For the algebra , we define a subset of W, of non-null density. We calculate explicitly all the Demazure polynomials for this subset.