Jacquet modules of strongly positive representations of the metaplectic group $\widetilde {Sp(n)}$

Abstract

Strongly positive discrete series represent a particularly important class of irreducible square-integrable representations of p-adic groups. Indeed, these representations are used as basic building blocks in known constructions of general discrete series. In this paper, we explicitly describe Jacquet modules of strongly positive discrete series. The obtained description of Jacquet modules, which relies on the classification of strongly positive discrete series given in [10], is valid in both classical and metaplectic case. We expect that our results, besides being interesting by themselves, should be relevant to some potential applications in the theory of automorphic forms, where both representations of metaplectic groups and structure of Jacquet modules play an important part.