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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Ivan Matić
Journal: Trans. Amer. Math. Soc. 365 (2013), 2755-2778
MSC (2010): Primary 22E35; Secondary 22E50
Published electronically: September 19, 2012
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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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Ivan Matić
Affiliation: Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia
Email: imatic@mathos.hr

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05725-4
PII: S 0002-9947(2012)05725-4
Keywords: Strongly positive discrete series, classical $p$-adic groups, metaplectic groups, Jacquet modules
Received by editor(s): February 14, 2011
Received by editor(s) in revised form: September 29, 2011
Published electronically: September 19, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.