On the Witten-Reshetikhin-Turaev representations of mapping class groups

Details On the Witten-Reshetikhin-Turaev representations of mapping class groups On the Witten-Reshetikhin-Turaev representations of mapping class groups

1997-01-30

arxiv.org/abs/q-alg/9701042v5

Mathematics

Quantum Algebra

AMS-TeX, 7 pages. Notational changes and typos corrected. To appear in Proc. A.M.S

Scientific paper

We consider a central extension of the mapping class group of a surface with a collection of framed colored points. The Witten-Reshetikhin-Turaev TQFTs associated to SU(2) and SO(3) induce linear representations of this group. We show that the denominators of matrices which describe these representation over a cyclotomic field can be restricted in many cases. In this way, we give a proof of the known result that if the surface is a torus and there are no colored points, the representations have finite image.

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