Translator Disclaimer
2015 Linear symplectomorphisms as $R$-Lagrangian subspaces
Chris Hellmann, Brennan Langenbach, Michael VanValkenburgh
Involve 8(4): 551-569 (2015). DOI: 10.2140/involve.2015.8.551

Abstract

The graph of a real linear symplectomorphism is an R-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely imaginary and may be expressed in terms of the generating function of the transformation. We provide explicit formulas; moreover, as an application, we give an explicit general formula for the metaplectic representation of the real symplectic group.

Citation

Download Citation

Chris Hellmann. Brennan Langenbach. Michael VanValkenburgh. "Linear symplectomorphisms as $R$-Lagrangian subspaces." Involve 8 (4) 551 - 569, 2015. https://doi.org/10.2140/involve.2015.8.551

Information

Received: 20 September 2013; Revised: 24 August 2014; Accepted: 31 October 2014; Published: 2015
First available in Project Euclid: 22 November 2017

zbMATH: 1380.37112
MathSciNet: MR3366010
Digital Object Identifier: 10.2140/involve.2015.8.551

Subjects:
Primary: 37J10, 51A50, 70H15, 81S10

Rights: Copyright © 2015 Mathematical Sciences Publishers

JOURNAL ARTICLE
19 PAGES


SHARE
Vol.8 • No. 4 • 2015
MSP
Back to Top