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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.

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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.

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  • $\begingroup$ The paper by Wenzl wins it. Admittedly, it's focused on the root of unity case, but contains exactly the generic stuff I needed. $\endgroup$
    – Ben Webster ♦
    Commented Oct 6, 2009 at 23:55
  • $\begingroup$ *-structures come in kinds, ones where q*=q (so q is behaving like a real number) and ones where q*=q^-1 (so q is behaving like a complex number of size one). So if the *-structure that you're coming up with is the latter kind that's saying that morally q is behaving like a root of unity (or at least like something of norm one) even though as a degree shift it makes no sense to set q to a complex number. $\endgroup$
    – Noah Snyder
    Commented Oct 10, 2009 at 1:44

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