The crystal base and Littelmann’s refined Demazure character formula

[K1] M. Kashiwara, <i>Crystalizing the $q$-analogue of universal enveloping algebras</i>, Comm. Math. Phys. <b>133</b> (1990), no. 2, 249–260.

[D] M. Demazure, <i>Désingularisation des variétés de Schubert généralisées</i>, Ann. Sci. École Norm. Sup. (4) <b>7</b> (1974), 53–88.

[K2] M. Kashiwara, <i>On crystal bases of the $q$-analogue of universal enveloping algebras</i>, Duke Math. J. <b>63</b> (1991), no. 2, 465–516.

[A] H. H. Andersen, <i>Schubert varieties and Demazure's character formula</i>, Invent. Math. <b>79</b> (1985), no. 3, 611–618.

[J] A. Joseph, <i>On the Demazure character formula</i>, Ann. Sci. École Norm. Sup. (4) <b>18</b> (1985), no. 3, 389–419.

[K3] M. Kashiwara, <i>Global crystal bases of quantum groups</i>, RIMS preprint 756, 1991.

[L] P. Littleman, <i>Crystal groups and Young tableaux</i>, preprint, 1991.

[M] O. Mathieu, <i>Formules de caractères pour les algèbres de Kac-Moody générales</i>, Astérisque (1988), no. 159-160, 267.

[SK] Shrawan Kumar, <i>Demazure character formula in arbitrary Kac-Moody setting</i>, Invent. Math. <b>89</b> (1987), no. 2, 395–423.

[RR] S. Ramanan and A. Ramanathan, <i>Projective normality of flag varieties and Schubert varieties</i>, Invent. Math. <b>79</b> (1985), no. 2, 217–224.