JANTZEN FILTRATION OF WEYL MODULES, PRODUCT OF YOUNG SYMMETRIZERS AND DENOMINATOR OF YOUNG'S SEMINORMAL BASIS

Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p > 0, Delta(lambda) denote the Weyl module of G of highest weight lambda and iota(lambda,mu) : Delta(lambda + mu) -> Delta(lambda) circle times Delta(mu) be the canonical G-morphism. We study the split condition for iota(lambda,mu) over Z((p)), and apply this as an approach to compare the Jantzen filtrations of the Weyl modules Delta(lambda) and Delta(lambda + mu). In the case when G is of type A, we show that the split condition is closely related to the product of certain Young symmetrizers and, under some mild conditions, is further characterized by the denominator of a certain Young's seminormal basis vector. We obtain explicit formulas for the split condition in some cases.