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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Asymptotic properties of the quantum representations of the modular group
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by Laurent Charles PDF
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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Additional Information
  • Laurent Charles
  • Affiliation: Institut de Mathématiques de Jussieu (UMR 7586), Université Pierre et Marie Curie – Paris 6, Paris, F-75005 France
  • MR Author ID: 662048
  • Received by editor(s): July 2, 2010
  • Received by editor(s) in revised form: December 20, 2010
  • Published electronically: June 5, 2012
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 364 (2012), 5829-5856
  • MSC (2010): Primary 57R56, 35S30, 14K25, 58J28, 58J37
  • DOI: https://doi.org/10.1090/S0002-9947-2012-05537-1
  • MathSciNet review: 2946934