On Demazure polynomials
For an affine Kac-Moody algebra \(\mathfrak g\), let \(\lambda\) be a dominant weight and \(w\) an element of the Weyl group. Denote by \(e_{w\lambda}\) an element of \(L(\lambda)_{w\lambda}\), where \(L(\lambda)\) is the unique irreducible \(\mathfrak g\)-module of highest weight \(\lambda\). The \(\mathfrak b\)-module generated by \(e_{w\lambda}\) is called the Demazure module denoted by \(E_w(\lambda)\), (\(\mathfrak b\) is the Borel subalgebra of \(\mathfrak g\)). The dimension of \(E_w(\lambda)\) is a polynomial in \(\lambda\). The author proves that this polynomial is harmonic. He also calculates explicitly all the Demazure polynomials for a subset \(\mathcal E\) of \(W\) in the case when \(\mathfrak g=\widehat{\mathfrak{sl}}\).
scientific article; zbMATH DE number 5118820