Parabolic induction and Jacquet functors for metaplectic groups

In this paper, we give a new formulation of a geometric lemma for the metaplectic groups over p-adic field F, analogous to the existing one for classical groups. This enables us to give a Zelevinsky type classification of irreducible admissible genuine representations of metaplectic groups. As an application of our Jacquet module technique, we explicitly calculate Jacquet modules of even and odd Weil representations.