On the Witten-Reshetikhin-Turaev representations of mapping class groups
q-alg
2015-12-22 v5 Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.q-alg/9701042,
title = {On the Witten-Reshetikhin-Turaev representations of mapping class groups},
author = {Patrick M. Gilmer},
journal= {arXiv preprint arXiv:q-alg/9701042},
year = {2015}
}
Comments
AMS-TeX, 7 pages. Notational changes and typos corrected. To appear in Proc. A.M.S