Given F a locally compact, nondiscrete, non-archimedean field of characteristic ≠ 2 and R an integral domain such that a non-trivial smooth character χ: F → R <sup>×</sup>exists, we construct the (reduced) metaplectic group attached to χ and R. We show that it is in the expected cases a double cover of the symplectic group over F. Finally, we define a faithful infinite dimensional R-representation of the metaplectic group analogue to the Weil representation in the complex case.
Chinello, G., Turchetti, D. (2015). Weil Representation and Metaplectic Groups over an Integral Domain. COMMUNICATIONS IN ALGEBRA, 43(6), 2388-2419 [10.1080/00927872.2014.893729].
Weil Representation and Metaplectic Groups over an Integral Domain
Chinello, Gianmarco
;
2015
Abstract
Given F a locally compact, nondiscrete, non-archimedean field of characteristic ≠ 2 and R an integral domain such that a non-trivial smooth character χ: F → R ×exists, we construct the (reduced) metaplectic group attached to χ and R. We show that it is in the expected cases a double cover of the symplectic group over F. Finally, we define a faithful infinite dimensional R-representation of the metaplectic group analogue to the Weil representation in the complex case.
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