Local Theory of Primitive Theta Functions |
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| Authors: | Atsushi Murase Takashi Sugano |
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| Institution: | (1) Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto, 603-8555, Japan;(2) Department of Mathematics, Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa, 920-1192, Japan |
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| Abstract: | 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)). |
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| Keywords: | Theta function Heisenberg group metaplectic representation |
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