Oriented Lagrangian planes and the metaplectic group

  • Gérard Lion
  • Michèle Vergne
Part of the Progress in Mathematics book series (PM, volume 6)


Let us consider \(c\left( {{{\ell }_{1}},{{\ell }_{2}},{{\ell }_{3}}} \right) = {{e}^{{ - \frac{{i\pi }}{4}\tau \left( {{{\ell }_{1}},{{\ell }_{2}},{{\ell }_{3}}} \right)}}}\) We will now show that there exists a function \(s({{\tilde{\ell }}_{1}},{{\tilde{\ell }}_{2}})\) defined on couples of oriented Lagrangian planes, invariant under the symplectic group, such that
$$ c{{({{\ell }_{1}},{{\ell }_{2}},{{\ell }_{3}})}^{2}} = s{{({{\tilde{\ell }}_{1}},{{\tilde{\ell }}_{2}},)}^{{ - 1}}}s{{({{\tilde{\ell }}_{2}},{{\tilde{\ell }}_{3}})}^{{ - 1}}}s{{({{\tilde{\ell }}_{3}},{{\tilde{\ell }}_{1}})}^{{ - 1}}}. $$
We will use this fact to prove that the Shale-Weil projective representation is a representation of the two-sheeted covering group G2 of G = Sp(B).


Symplectic Group Projective Representation Operational Calculus Oriented Plane Dual Vector Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Gérard Lion
    • 1
  • Michèle Vergne
    • 2
  1. 1.X U.E.R. de Sciences EconomiquesUniversité de ParisNanterreFrance
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations