English

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