Weil representations and metaplectic groups over an integral domain
Representation Theory
2013-09-23 v1 Number Theory
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.
Cite
@article{arxiv.1309.5181,
title = {Weil representations and metaplectic groups over an integral domain},
author = {Gianmarco Chinello and Daniele Turchetti},
journal= {arXiv preprint arXiv:1309.5181},
year = {2013}
}