Abstract
Let G n denote either the group Sp(n, F) or SO(2n + 1, F) over a local non-archimedean field F. We study representations of segment type of group G n , which play a fundamental role in the constructions of discrete series, and obtain a complete description of the Jacquet modules of these representations. Also, we provide an alternative way for determination of Jacquet modules of strongly positive discrete series and a description of top Jacquet modules of general discrete series.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arthur, J.: The Endoscopic Classification of Representations, vol. 61 of American Mathematical Society Colloquium Publications. American Mathematical Society, Providence, RI (2013). Orthogonal and symplectic groups
Jantzen C.: Tempered representations for classical p-adic groups. Manuscr. Math. 145, 319–387 (2014)
Kret A., Lapid E.: Jacquet modules of ladder representations. C. R. Math. Acad. Sci. Paris 350, 937–940 (2012)
Lapid E., Mínguez A.: On a determinantal formula of Tadić. Am. J. Math. 136, 111–142 (2014)
Matić I.: Strongly positive representations of metaplectic groups. J. Algebra 334, 255–274 (2011)
Matić I.: Jacquet modules of strongly positive representations of the metaplectic group \({\widetilde{Sp(n)}}\) . Trans. Am. Math. Soc. 365, 2755–2778 (2013)
Matić, I.: On Jacquet Modules of Discrete Series: The First Inductive Step. preprint (2014)
Mœglin C.: Sur la classification des séries discrètes des groupes classiques p-adiques: paramètres de Langlands et exhaustivité. J. Eur. Math. Soc. 4, 143–200 (2002)
Mœglin C., Tadić M.: Construction of discrete series for classical p-adic groups. J. Am. Math. Soc. 15, 715–786 (2002)
Muić G.: Composition series of generalized principal series; the case of strongly positive discrete series. Isr. J. Math. 140, 157–202 (2004)
Silberger A.J.: Special representations of reductive p-adic groups are not integrable. Ann. Math. 111(2), 571–587 (1980)
Tadić M.: Structure arising from induction and Jacquet modules of representations of classical p-adic groups. J. Algebra 177, 1–33 (1995)
Tadić M.: On reducibility of parabolic induction. Isr. J. Math. 107, 29–91 (1998)
Tadić, M.: Square integrable representations of classical p-adic groups corresponding to segments. Represent. Theory 3, 58–89 (1999); (electronic)
Tadić M.: On invariants of discrete series representations of classical p-adic groups. Manuscr. Math. 135, 417–435 (2011)
Tadić M.: On tempered and square integrable representations of classical p-adic groups. Sci. China Math. 56, 2273–2313 (2013)
Zelevinsky A.V.: Induced representations of reductive p-adic groups. II. On irreducible representations of GL(n). Ann. Sci. école Norm. Sup. 13(4), 165–210 (1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Matić, I., Tadić, M. On Jacquet modules of representations of segment type. manuscripta math. 147, 437–476 (2015). https://doi.org/10.1007/s00229-015-0727-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00229-015-0727-9