TITLE: Are there interesting monoidal structures on representations of quantum affine algebras?
QUESTION [6 upvotes]: Is there a good monoidal structure on a category of integrable representations of a quantum affine algebra?  In the ordinary affine Kac-Moody case, there is the usual tensor product (symmetric, adds charges) and a fusion structure (braided, comes from G-bundles on curves, preserves central charge).  In the quantum case, there is the usual tensor product (braided meromorphic-braided$^\ast$), but all I see in the literature about fusion is vague comments that it can't exist.  I guess my question should be "what is the major malfunction?"
$^\ast$ Edit: The meromorphic property (in the sense of Soibelman's Meromorphic tensor categories) seems to be a first hint at problems, and I should have paid better attention to it.

REPLY [4 votes]: The poles of the R-matrices for quantum affine algebras are the price to pay for the abovementioned simplification - the braiding becomes symmetric under q-deformation. 
If there were no poles, the category would have been symmetric and hence would be a representation category of a (usual) group. In fact, the poles of the R-matrices contain much of the information about the structure of this category. 
Also, I'd like to add that there is an interesting paper by Hernandez, math/0504269, where he discusses a new "fusion" tensor product on representations of quantum affine algebras.