Braid Group Actions and Tensor Products
Quantum Algebra
2007-05-23 v1 Representation Theory
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 --matrix has a zero.
Keywords
Cite
@article{arxiv.math/0106241,
title = {Braid Group Actions and Tensor Products},
author = {Vyjayanthi Chari},
journal= {arXiv preprint arXiv:math/0106241},
year = {2007}
}
Comments
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