Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Asymptotic properties of the quantum representations of the modular group


Author: Laurent Charles
Journal: Trans. Amer. Math. Soc. 364 (2012), 5829-5856
MSC (2010): Primary 57R56, 35S30, 14K25, 58J28, 58J37
Published electronically: June 5, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 57R56, 35S30, 14K25, 58J28, 58J37

Retrieve articles in all journals with MSC (2010): 57R56, 35S30, 14K25, 58J28, 58J37


Additional Information

Laurent Charles
Affiliation: Institut de Mathématiques de Jussieu (UMR 7586), Université Pierre et Marie Curie – Paris 6, Paris, F-75005 France

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05537-1
PII: S 0002-9947(2012)05537-1
Received by editor(s): July 2, 2010
Received by editor(s) in revised form: December 20, 2010
Published electronically: June 5, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.