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arXiv · 1309.5181

Weil representations and metaplectic groups over an integral domain

Gianmarco Chinello·Daniele Turchetti
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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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Gianmarco Chinello, Daniele Turchetti. 2013-09-20. Weil representations and metaplectic groups over an integral domain. https://arxiv.org/abs/1309.5181

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