TITLE: What is the "right" hermitian structure on tensor products of quantum group representations?
QUESTION [5 upvotes]: This is pretty specific, but there are some experts around.
So, in Chari & Pressley, it's explained that in the standard *-structure, every irreducible, finite-dimensional representation of a quantum group (at a generic parameter) is unitary.  Is it written somewhere what the "right" unitary structure on a tensor product of these representations is?  
I ask because if one categorifies such representations, one gets a unitary structure essentially for free, so it would extremely useful if someone had already written down one I could match up with.

REPLY [4 votes]: I know these are all about the root of unity case, but you might look at this paper by Kirillov, and this one by Wenzl.