The Zelevinsky classification of unramified representations of the metaplectic group

In this paper a Zelevinsky type classification of genuine unramified irreducible representations of the metaplectic group over a p  -adic field with p≠2p≠2 is obtained. The classification consists of three steps. Firstly, it is proved that every genuine irreducible unramified representation is a fully parabolically induced representation from unramified characters of general linear groups and a genuine irreducible negative unramified representation of a smaller metaplectic group. Genuine irreducible negative unramified representations are described in terms of parabolic induction from unramified characters of general linear groups and a genuine irreducible strongly negative unramified representation of a smaller metaplectic group. Finally, genuine irreducible strongly negative unramified representations are classified in terms of Jordan blocks. The main technical tool is the theory of Jacquet modules.