Asymptotic properties of the quantum representations of the modular group

Laurent Charles

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arXiv · 1005.3447

Asymptotic properties of the quantum representations of the modular group

Laurent Charles

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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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Laurent Charles. 2010-05-19. Asymptotic properties of the quantum representations of the modular group. https://arxiv.org/abs/1005.3447

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