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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo


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A reverse engineering approach to the Weil representation

1I.M.J.-P.R.G. (U.M.R. 7586 du C.N.R.S.), Université Pierre et Marie Curie, 4 place Jussieu, 75005, Paris, France

2Department of Mathematics, University of Oklahoma, Norman, OK, 73019, USA

© 2014 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Open Mathematics. Volume 12, Issue 10, Pages 1500–1585, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-014-0428-8, June 2014

Publication History

Published Online:
2014-06-21

Abstract

We describe a new approach to the Weil representation attached to a symplectic group over a finite or a local field. We dissect the representation into small pieces, study how they work, and put them back together. This way, we obtain a reversed construction of that of T. Thomas, skipping most of the literature on which the latter is based.

MSC: 22E45; 20C33; 22E46

Keywords: Weil representation; Oscillator representation; Metaplectic representation

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