Weil representation and metaplectic groups over an integral domain

Gianmarco Chinello (1) , Daniele Turchetti (2)

1 Algèbre et Géometrie
2 LMV - Laboratoire de Mathématiques de Versailles

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.

Mots clés: metaplectic group; Weil representation; modular representations

Domaines: Théorie des représentations [math.RT]; Théorie des nombres [math.NT]

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