## Overview

My research involves the representation theory of groups. I am particularly interested in symmetric groups and general linear groups and the combinatorics associated with them. A series of my papers has been concerned with evaluating decomposition numbers of various groups and establishing patterns in the decomposition matrices.

I also study q-analogues of the symmetric group algebra, especially Hecke algebras and q-Schur algebras. A collection of fundamental papers has established the relationship between repesentations of general linear groups in both the describing and non-describing characteristic cases and repesentations of symmetric groups. The main key in this area is the q-Schur algebra, which was introduced by R. Dipper and me.

## Research Student Supervision

Heyfron,P, Positive functions defined on Hermitian positive semidefinite matrices

Honey,G

Law,KWT, Results on the decomposition matrices of symmetric groups

Lyle,S, Some topics in the representation theory of the symmetric and general linear groups

McNulty,K, Matrix functions on Hermitian positive semidefinite matrices and totally positive matrices

Pallikaros,C, Representations of Hecke algebras of type D_n

Papamichael,E, Generalised matrix functions on M-matrices

Reuter,A, The submobile structure of Specht modules

Richards,MJ, Some decomposition numbers for Hecke algebras of general linear groups

Williams,A