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in "Jaeger’s Higman-Sims state model and the B2 spider" by Greg Kuperberg (arxiv:math9601221v1, 1996) there are some quantum dimensions listed in the "Discussion" part. Evidently quantum groups (q-deformed Hopf algebras if I read correctly) have representations, and those representations have quantum dimensions, and those can computed by some Weyl formula. Yup, I can parrot the lingo :-) but I couldn't compute an actual quantum dimension even at gunpoint.
Now there is a deep connection between quantum algebras and knot theory. I'm an amateur dabbling in knot theory and alone knowing some quantum dimensions (which "are", by the connection, the value of a knot polynome for a single loop) for assorted groups and representations would be invaluable for my project of classifying S matrices. (Example: For the group G2 the result is q^5+q^4+q+1+1/q+1/q^4+1/q^5, and armed with nothing more than this knowledge, I could construct an Kauffman abstract tensor model for Kuperbergs G2 invariant. It's no impressive result, any expert could do this using higher math, but I did it just with some tensor equations even I can understand.)

Kuperbergs paper(s) was the only one I know where explicite values for quantum dimensions were given at all, thus my plea: Can somebody compute quantum dimensions for me? The classification of simple groups is complete, so if there are finitely many representations too (I don't know) it's a finite task :-) A reference suffices too...if my university has the book.

Hauke Reddmann

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I'd recommend first learning the Weyl dimension formula for non-quantum groups (say by reading Fulton+Harris). Anyway, Scott Morrison's quantum groups package (see can compute this for any particular rep that you want. – Noah Snyder Dec 11 '10 at 19:56
THX! I recently installed Mathematica 7 so this should be no great problem. (But still, mind to email me some sample function call, say, G2 and the rep for the G2 invariant, to my email address fc3a501(at) I'm still a beginner at Mathematica and if I have to decompile the package for finding that call WeylDimension[group,rep] - or whatever it's called...) Question answered. Hauke – Hauke Reddmann Dec 13 '10 at 19:11

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