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.