Let K be an algebraically closed field of finite characteristic p, and let be an integer. In the paper, we give a character formula for all simple rational representations of with highest weight any multiple of any fundamental weight. Our formula is slightly more general: say that a dominant weight 5 is special if there are integers such that and . Indeed, we compute the character of any simple module whose highest weight 5 can be written as with all are special. By stabilization, we get a character formula for a family of irreducible rational -modules.
Cite this article
Athanase Papadopoulos, O. Mathieu, A character formula for a family of simple modular representations of . Comment. Math. Helv. 74 (1999), no. 2, pp. 280–296DOI 10.1007/S000140050089