The crystal base and Littelmann's refined Demazure character formula (Q1320618)

Demazure's character formula describes the weight multiplicities of the \(U({\mathfrak n}^ +)\)-module generated by an extremal vector of the irreducible highest weight \(U({\mathfrak g})\)-module, where \({\mathfrak g}\) is a symmetrizable Kac-Moody Lie algebra. In his paper [Crystal graphs and Young tableaux (preprint)], \textit{P. Littelmann} gives a conjecture of a generalization of the Demazure character formula which is described by crystal bases. In this paper the author proves this conjecture for any symmetrizable case.