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.(more)
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%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
}