# Are there interesting monoidal structures on representations of quantum affine algebras?

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.

• I don't really think ordinary tensor products are boring. I should change it to a more judgment-neutral word. – S. Carnahan Oct 12 '09 at 6:38