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
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