User:John Z/drafts/Weil representation

The Weil representation is a representation of the Metaplectic group, the two fold cover of a Symplectic group Sp(n) over the reals of dimension n >1, which has a nontrivial fundamental group but as an algebraic group has no finite group extension. It was introduced byAndre Weil in Sur Certaines Groupes d'Operateurs Unitaires.