Asymptotic properties of the quantum representations of the modular group

Charles, Laurent

doi:10.1090/S0002-9947-2012-05537-1

Asymptotic properties of the quantum representations of the modular group
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Trans. Amer. Math. Soc. 364 (2012), 5829-5856 Request permission

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.

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