Weil representation and metaplectic groups over an integral domain

Abstract : Given F a locally compact, non-discrete, non-archimedean field of characteristic different from 2 and R an integral domain such that a non-trivial smooth F-character with values in the multiplicative group of R exists, we construct the (reduced) metaplectic group attached to R. We show that it is in most 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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  • HAL Id : hal-00860947, version 1
  • ARXIV : 1309.5181

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Gianmarco Chinello, Daniele Turchetti. Weil representation and metaplectic groups over an integral domain. 2013. ⟨hal-00860947⟩

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