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Local Theory of Primitive Theta Functions

Published online by Cambridge University Press:  04 December 2007

Atsushi Murase  and
Takashi Sugano
Atsushi Murase
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto 603-8555, Japan. E-mail: murase@cc.kyoto-su.ac.jp
Takashi Sugano
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan. E-mail: sugano@kappa.s.kanazawa-u.ac.jp
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Abstract

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We study primitive theta functions, which were first introduced by Shintani, in a purely local setting. We investigate a metaplectic representation of U(1) acting on the space of local primitive theta functions and give its explicit irreducible decomposition. As a by-product, we give a new proof of epsilon dichotomy for (U(1),U}(1)).

Keywords

Theta functionHeisenberg groupmetaplectic representation
Type
Research Article
Information
Compositio Mathematica , Volume 123 , Issue 3 , September 2000 , pp. 273 - 302
Copyright
© 2000 Kluwer Academic Publishers