Abstract
We have constructed in Part 1 a projective representation R of the symplectic group. As discovered by A. Weil, this representation plays a central role in the transformation properties of the classical Jacobi θ-serie \(\theta (z) = \sum\limits_{n} {{{e}^{{i\pi {{n}^{2}}z}}}}\) and higher dimensional θ-series, when interpreted as suitable coefficients of this representation R. We indicate now the nature of the relation between R and theta series:
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Let D be the Siegel upper half-plane, i.e.
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D = {Z. (n × n) complex symmetric matrices, such that Im Z ≫ 0}
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© 1980 Springer Science+Business Media New York
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Lion, G., Vergne, M. (1980). Introduction. 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_11
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DOI: https://doi.org/10.1007/978-1-4684-9154-8_11
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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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