Jacquet modules of strongly positive representations of the metaplectic group
Author:
Ivan Matić
Journal:
Trans. Amer. Math. Soc. 365 (2013), 27552778
MSC (2010):
Primary 22E35; Secondary 22E50
Published electronically:
September 19, 2012
MathSciNet review:
3020114
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Abstract: Strongly positive discrete series represent a particularly important class of irreducible squareintegrable 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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 , Notes on the local theta correspondence (lectures at the European School in Group Theory),(1996).
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 Colette Mœglin and Marko Tadić, Construction of discrete series for classical adic groups, J. Amer. Math. Soc. 15 (2002), no. 3, 715786. MR 1896238 (2003g:22020)
 13.
 Goran Muić, Composition series of generalized principal series; the case of strongly positive discrete series, Israel J. Math. 140 (2004), 157202. MR 2054843 (2005e:22018)
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 , On the nonunitary unramified dual for classical adic groups, Trans. Amer. Math. Soc. 358 (2006), no. 10, 46534687. MR 2231392 (2007j:22029)
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 Marko Tadić, Structure arising from induction and Jacquet modules of representations of classical adic groups, J. Algebra 177 (1995), no. 1, 133. MR 1356358 (97b:22023)
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 , On reducibility of parabolic induction, Israel J. Math. 107 (1998), 2991. MR 1658535 (2001d:22012)
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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:
http://dx.doi.org/10.1090/S000299472012057254
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.
