We show that the complexity of the Lie module Lie(n) in characteristic p is bounded above by m, where pm is the largest p-power dividing n, and, if n is not a p-power, is equal to the maximum of the complexities of Lie(pi) for 1≤i≤m.

Filtrations of modules over wreath products of algebras are studied and corresponding multiplicity formulas are given in terms of Littlewood–Richardson coefficients. An example relevant to Jantzen filtrations in Schur algebras is presented.

We study Rouquier blocks of symmetric groups and Schur algebras in detail, and obtain explicit descriptions 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, Lascoux–Leclerc–Thibon–Rouquier and James for these blocks.

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.

In this paper, we construct the Ext-quivers of the principal blocks of F[Sfr ]11 and F[Sfr ]12, where F is an algebraically closed field of characteristic 3. We also obtain the Loewy structures of three principal indecomposable modules of the principal block of F[Sfr ]11.