Asymptotic properties of the quantum representations of the modular group
Geometric Topology
2010-05-20 v1 Mathematical Physics
math.MP
Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.1005.3447,
title = {Asymptotic properties of the quantum representations of the modular group},
author = {Laurent Charles},
journal= {arXiv preprint arXiv:1005.3447},
year = {2010}
}
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38 pages