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 λ is special if there are integers such that and . Indeed, we compute the character of any simple module whose highest weight λ can be written as with all are special. By stabilization, we get a character formula for a family of irreducible rational -modules.

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