Abstract

Let G be a semisimple, simply connected algebraic group defined over an algebraically closed field k of positive characteristic p. Assume that is larger than the Coxeter number of G and that the Lusztig character formula holds for regular restricted dominant weights. In this paper, we introduce two new highest weight categories C reg and C reg, both full subcategories of the category C of rational G-modules. The standard and costandard modules for these categories arise from reduction mod p from the quantum enveloping algebra associated to G.

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