Abstract
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
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).
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© 1980 Springer Science+Business Media New York
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Lion, G., Vergne, M. (1980). Oriented Lagrangian planes and the metaplectic group. In: The Weil representation, Maslov index and Theta series. Progress in Mathematics, vol 6. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4684-9154-8_8
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DOI: https://doi.org/10.1007/978-1-4684-9154-8_8
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Publisher Name: Birkhäuser, Boston, MA
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Online ISBN: 978-1-4684-9154-8
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