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.



What is the "right" hermitian structure on tensor products of quantum group representations?
I know these are all about the root of unity case, but you might look at [this paper](http://www.ams.org/mathscinet-getitem?mr=1358983) by Kirillov, and [this one](http://www.ams.org/mathscinet-getitem?mr=1470857) by Wenzl.


