  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.

Representation Theory;Number Theory