Weil representations and metaplectic groups over an integral domain

2013/09/20 by Gianmarco Chinello, Chinello, Gianmarco, Danièle Turchetti +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1309.5181

openalex publication_date 2013/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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