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In this paper, what is already known about defect 2 blocks of symmetric groups is used to deduce information about the corresponding blocks of Schur algebras. This information includes Ext-quivers and decomposition numbers, as well as Loewy structures of the Weyl modules, principal indecomposable modules and tilting modules.

Abstract. We study Rouquier blocks of symmetric groups and Schur algebras in detail, and obtain explicit description for the radical layers of the principal indecomposable, Weyl, Young and Specht modules of these blocks. At the same time, the Jantzen filtrations of the Weyl modules are shown to coincide with their radical filtrations. We also address the conjectures of Martin, LascouxLeclerc-Thibon-Rouquier and James for these blocks.

Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p > 0, ∆(λ) denote the Weyl module of G of highest weight λ and ι λ,µ : ∆(λ+µ) → ∆(λ)⊗∆(µ) be the canonical G-morphism. We study the split condition for ι λ,µ over Z (p) , and apply this as an approach to compare the Jantzen filtrations of the Weyl modules ∆(λ) and ∆(λ + µ). 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 is further characterized by the denominator of a certain Young's seminormal basis vector in certain cases. We obtain explicit formulas for the split condition in some cases.

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