My main area of interest and expertise is the representation theory of Coxeter groups, Iwahori-Hecke algebras and Schur algebras. Recently my work has focused on the modular representation theory of the Ariki-Koike algebras and the associated cyclotomic q-Schur algebras. This theory is intimately connected with the representation theory of affine Hecke algebras and quantum groups; there are also ramifications for the representation theory of the symmetric groups and finite reductive groups.
Other active interests include:
* Cyclotomic Hecke algebras, complex reflection groups and their braid groups.
* The q-Schur algebras and cyclotomic q-Schur algebras.
* Combinatorics of symmetric groups and Hecke algebras.
* The theory of Cellular algebras.
* Affine Hecke algebras.
* Quantum groups, canonical bases, and crystal graphs.
* Kazhdan-Lusztig polynomials and cell representations.
* Coxeter groups and groups of Lie type, and their representation theory.
