Abstract
Let ℓ1, ℓ2, ℓ3 be three Lagrangian planes in the symplectic vector space (V, B). We consider the canonical unitary intertwining operator (we leave implicit the choice of e1, e2, e3):
which intertwines W(ℓj) and W(ℓi) defined in 1.4.8. It is clear that the operator Ƒ1,3 Ƒ3,2 Ƒ2,1 is proportional to the identity operator on H(ℓ1) as this operator intertwines the irreducible representation W(ℓ1) with itself. Hence there is a scalar of modulus one a(ℓ1, ℓ2, ℓ3) such that:
(It is easy to see that a (l 1, ℓ2, ℓ3) does not depend of e1, e2, e3.)
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© 1980 Springer Science+Business Media New York
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Lion, G., Vergne, M. (1980). The cocycle of the Shale-Weil representation and the Maslov index. 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_7
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DOI: https://doi.org/10.1007/978-1-4684-9154-8_7
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Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-0-8176-3007-2
Online ISBN: 978-1-4684-9154-8
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