Rowena E. Paget

Minimal and maximal constituents of twisted Foulkes characters

We prove combinatorial rules that give the minimal and maximal partitions labelling the irreducible constituents of a family of characters for the symmetric group that generalize Foulkes permutation characters. Restated in the language of symmetric functions, our results determine all minimal and maximal partitions that label Schur functions appearing in the plethysms

The Mullineux Map for RoCk Blocks

s_\nu \circ s_{(m)}

Cohomological stratification of diagram algebras

. As a corollary we prove two conjectures of Agaoka on the lexicographically least constituents of the plethysms

Young modules and filtration multiplicities for Brauer algebras

s_\nu \circ s_{(m)}

Set families and Foulkes modules

and

A family of modules with Specht and dual Specht filtrations

s_\nu \circ s_{(1^m)}

Brauer Algebras with Parameter n = 2 Acting on Tensor Space

.

Representation theory of q-rook monoid algebras

We study the effect of tensoring simple modules in RoCK blocks (also known as Rouquier blocks) of symmetric groups with the one-dimensional sign representation, and the analogue for Hecke algebras of type A. We find an explicit and very neat description. We also describe p-regularization for partitions in these blocks.