Mathematics Department Head of Department

Prof AN Pressley Department of Mathematics King's College London Strand, London WC2R 2LS United Kingdom Room 430, Strand Building Tel: +44-(0)207-8482975 (direct) Tel: +44-(0)207-8482216 (general office) Fax: +44-(0)207-8482017 E-mail: andrew.pressley.AT.kcl.ac.uk

Member of the Lie Theory andGeometry Group

Research Interests

I am interested in quantum groups, a relatively new kind of algebraic structure which can be viewed as a generalization of the ordinary notion of a group and becomes that notion when a certain parameter in the theory tends to zero. (For those interested in Physics, this is analogous to the way that the predictions of quantum mechanics approach those of classical mechanics if Planck's constant tends to zero - and this is the origin of the name quantum group.) The study of quantum groups as mathematical objects began around 1985, although examples had appeared earlier in the Physics literature. Since then, they have been studied intensively and have proved to have unexpected relation to a number of other fields, such as the theory of knots. Their study has also led to the resolution of a number of long-standing open problems in ordinary group theory.

Recent Publications

• "An Algebraic characterization of the affine canonical basis", J Beck, V Chari and AN Pressley, Duke Math.J.99 (1999) 455-487.
• "Quantum affine algebras at roots of unity", V Chari and AN Pressley, Representation Theory 1 (1997) 280-328.
• "Minimal affinizations of representations of quantum groups: the simply-laced case.", V Chari and AN Pressley, J. Algebra 184 (1996) 1-30.
• "Yangians, integrable quantum systems and Dorey's rule.", V Chari and AN Pressley, Commun. Math. Phys. 181 (1996) 265-302.