Gradings in Modular Representations

This paper considers Weyl modules for a simple, simply connected algebraic group over an algebraically closed field k of positive characteristic p. The main result proves that Weyl modules have (cogood) p-filtrations subject to restrictions on p. In case the high weight of the Weyl module is p-regular, the p-filtration is compatible with theG1-radical series of the module. This is a preliminary version, invoking the assumption that p≫ h, the Coxeter number of G. We expect later to replace this condition by two conditions, that p ≥ 2h − 2 and that p is sufficiently large that the Lusztig character formula holds for all restricted irreducible modules.