Jacquet modules of strongly positive representations of the metaplectic group

Author:
Ivan Matić

Journal:
Trans. Amer. Math. Soc. **365** (2013), 2755-2778

MSC (2010):
Primary 22E35; Secondary 22E50

Published electronically:
September 19, 2012

MathSciNet review:
3020114

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Abstract | References | Similar Articles | Additional Information

Abstract: Strongly positive discrete series represent a particularly important class of irreducible square-integrable representations of -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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Additional Information

**Ivan Matić**

Affiliation:
Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, Osijek, Croatia

Email:
imatic@mathos.hr

DOI:
https://doi.org/10.1090/S0002-9947-2012-05725-4

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.