Combinatorial results on Demazure modules
If \(\mathfrak{g}\) is a symmetrizable Kac-Moody algebra, \(\mathfrak{b}\) a Borel subalgebra, \(\lambda\) a dominant weight, and \(w\) an element of the Weyl group of \(\mathfrak{g}\), the subspace \[ E_w(\lambda) = U(w\mathfrak{b} w^{-1})v_\lambda \] of the highest weight module \(V(\lambda)\) is the Demazure module. There exists a natural bijection between \(\mathcal(P)(n)\) and a set of paths as defined by \textit{P. Littelmann} [Invent. Math. 116, 329-346 (1994; Zbl 0805.17019)].
scientific article; zbMATH DE number 1214130