Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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.

share|improve this question

1 Answer 1

up vote 3 down vote accepted

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.

share|improve this answer
    
The paper by Wenzl wins it. Admittedly, it's focused on the root of unity case, but contains exactly the generic stuff I needed. –  Ben Webster Oct 6 '09 at 23:55
    
*-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. –  Noah Snyder Oct 10 '09 at 1:44

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.