Irreducible Representations of Braid Groups via Quantized Enveloping Algebras

Abstract

Quantized enveloping algebrasU(g) and their representations provide natural settings for the action of the corresponding braid groups. Objects of particular interest are the zero weight spaces ofU(g)-modules since they are stable under the braid group action. We show that for g=slnthere is a class of simpleU(sln)-modules for which the action of the Artin braid groupBnon the zero weight space is irreducible.