ºÚÁÏÍø´óʼÇ

Abstract

Casimir elements play a central role in the representation theory of Lie algebras. They generate the centre of the universal enveloping algebra and act by scalar multiplication on every finite-dimensional simple module. For quantum groups, the standard quadratic quantum Casimir has been known since the early days of the theory, but higher-order analogues--quantum counterparts of the classical Gelfand invariants--have remained less well understood.

Ìý

In this talk, I will present recent work on the higher-order Casimir elements for quantum groups of classical types.Ìý I will explain how these elements generate the centre of the quantum group, and describe their Harish-Chandra images in terms of irreducible characters associated with hook partitions. This is joint work with Yanmin Dai.