Research interests
All of my research is related to Representation Theory - the study of the ways in which certain (algebraic) objects can act on others. We start with an algebra, and consider the possible ways in which this can act linearly on a vector space in a manner compatible with the algebra structure. Vector spaces with such actions are called modules. This is a very large, and important, area of research in Algebra, and I concentrate on two particular aspects: representations of algebraic groups and of "diagram" algebras. Although these problems arise in very different ways, and typically involve very different styles of proof, they are in fact closely related.
Algebraic Lie theory
The following schematic diagram indicates how my various reseach interests relate to some of the principal areas of Pure Mathematics (Geometry, Combinatorics, and Algebra) and Physics. Very loosely, we can refer to this common area as Algebraic Lie Theory. Clicking on a topic will provide more information on it.
As this very rough diagram should suggest, there is a rich interplay between the various topics, and hence we have at our disposal a wide variety of tools coming from the different disciplines. The freedom to switch freely between algebraic, geometric, and combinatorial points of view (while keeping in mind some of the physical motivation) is one of the most powerful features of research in this area. This connectivity also ensures that any results obtained have a wide variety of applications.
Anton Cox
(A.G.Cox@city.ac.uk)
Last modified: Tue 10 Jan 2006