Jacquet modules of strongly positive representations of the metaplectic group ̃𝑆𝑝(𝑛)

Matić, Ivan

doi:10.1090/S0002-9947-2012-05725-4

Jacquet modules of strongly positive representations of the metaplectic group $\widetilde {Sp(n)}$
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Trans. Amer. Math. Soc. 365 (2013), 2755-2778 Request permission

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 our earlier paper on metaplectic groups, is valid in both the classical and the metaplectic cases. 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 the structure of Jacquet modules play an important part.

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