%0 Generic %1 Charles2010 %A Charles, Laurent %D 2010 %K asymptotic modular quantum representations %T Asymptotic properties of the quantum representations of the modular group %U http://arxiv.org/abs/1005.3447 %X We study the asymptotic behaviour of the quantum representations of the modular group in the large level limit. We prove that each element of the modular group acts as a Fourier integral operator. This provides a link between the classical and quantum Chern-Simons theories for the torus. From this result we deduce the known asymptotic expansion of the Witten-Reshetikhin-Turaev invariants of the torus bundles with hyperbolic monodromy.

@misc{Charles2010, abstract = { We study the asymptotic behaviour of the quantum representations of the modular group in the large level limit. We prove that each element of the modular group acts as a Fourier integral operator. This provides a link between the classical and quantum Chern-Simons theories for the torus. From this result we deduce the known asymptotic expansion of the Witten-Reshetikhin-Turaev invariants of the torus bundles with hyperbolic monodromy. }, added-at = {2010-05-20T08:22:19.000+0200}, author = {Charles, Laurent}, biburl = {https://www.bibsonomy.org/bibtex/249a2010324b031d1f4c89869c1cd98ff/uludag}, description = {[1005.3447] Asymptotic properties of the quantum representations of the modular group}, interhash = {3f965d22f2530fc7814c990bce17959c}, intrahash = {49a2010324b031d1f4c89869c1cd98ff}, keywords = {asymptotic modular quantum representations}, note = {cite arxiv:1005.3447 Comment: 38 pages}, timestamp = {2010-05-20T08:22:19.000+0200}, title = {Asymptotic properties of the quantum representations of the modular group}, url = {http://arxiv.org/abs/1005.3447}, year = 2010 }