Braid Group Actions and Tensor Products

Abstract

We define an action of the braid group of a simple Lie algebra on the space of imaginary roots in the corresponding quantum affine algebra. We then use this action to determine an explicit condition for a tensor product of arbitrary irreducible finite--dimensional representations is cyclic. This allows us to determine the set of points at which the corresponding $R$--matrix has a zero.

This paper is an expanded version of math.qa/0012116. The results are stronger, and the conditions implied by the braid group action are made explicit