Translation cokernels of rational modules

A fundamental approach to the homological algebra of rational modules in positive characteristic p should begin with the translation properties of injective modules. This point of view leads to the study of functors related to coherent translation and their effect on the injective indecomposable modules indexed by p-regular dominant weights. The main result shows that the calculation can often be reduced to a corresponding calculation on the principal indecomposable modules of the Frobenius kernel. ^{1 1}1991 Mathematics Subject Classification: 20G05