Kai Meng Tan

Filtrations in Rouquier blocks of symmetric groups and Schur algebras

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.

Representations of wreath products of algebras

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.

Row and column removal in the q-deformed Fock space

Analogues of Jamess row and column removal theorems are proved for the q-decomposition numbers arising from the canonical basis in the q-deformed Fock space.

Kleshchev's decomposition numbers and branching coefficients in the Fock space

We give combinatorial descriptions of some coefficients of the canonical basis of the q-deformed Fock space representation of Uq(sle) and of some matrix entries for the action of the Chevellay generators fr with respect to the canonical basis. These are q-analogues of results of Kleshchev on decomposition numbers and branching coefficients for symmetric groups and Schur algebras.

The Complexity of the Lie Module

We show that the complexity of the Lie module

Sign sequences and decomposition numbers

\mathrm{Lie}(n)

The complexities of some simple modules of the symmetric groups

in characteristic

Homomorphisms from Specht Modules to Signed Young Permutation Modules

p

Modular representation theory of finite and p-adic groups

is bounded above by

Defect 3 Blocks of Symmetric Group Algebras

m