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Linear
symplectomorphisms as $R$-Lagrangian subspaces
Chris Hellmann, Brennan Langenbach and Michael VanValkenburgh
Vol. 8 (2015), No. 4, 551–569
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Abstract |
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The graph of a real linear symplectomorphism is an -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. |
Keywords
complex symplectic linear algebra, linear
symplectomorphisms, Lagrangian submanifolds, the
metaplectic representation
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Mathematical Subject Classification 2010
Primary: 37J10, 51A50, 70H15, 81S10
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Milestones
Received: 20 September 2013
Revised: 24 August 2014
Accepted: 31 October 2014
Published: 23 June 2015
Communicated by Ravi Vakil
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Authors |
| Chris Hellmann | |
| Department of Mathematics and
Statistics Grinnell College Grinnell, IA 50112 United States |
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| Brennan Langenbach | |
| Department of Mathematics and
Statistics Grinnell College Grinnell, IA 50112 United States |
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| Michael VanValkenburgh | |
| Department of Mathematics and
Statistics California State University Sacramento, CA 95819 United States |
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