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Duality for classical $p$-adic groups: The half-integral case


Author: Chris Jantzen
Journal: Represent. Theory 22 (2018), 160-201
MSC (2010): Primary 22E50
DOI: https://doi.org/10.1090/ert/519
Published electronically: October 24, 2018
MathSciNet review: 3868005
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Abstract: Let $G$ be a classical $p$-adic group and let $\pi$ be a smooth irreducible representation of $G$. In this paper, we consider the problem of calculating the dual (in the sense of Aubert and Schneider-Stuhler) $\hat {\pi }$. More precisely, if $\pi$ is specified by its Langlands data, the problem is to determine the Langlands data for $\hat {\pi }$. This problem reduces (based on supercuspidal support) to two main cases: half-integral reducibility and integral reducibility; the latter is addressed here.


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Additional Information

Chris Jantzen
Affiliation: Department of Mathematics, East Caronlina University, Greenville, North Carolina 27858
MR Author ID: 316181
Email: jantzenc@ecu.edu

Received by editor(s): January 15, 2018
Received by editor(s) in revised form: July 19, 2018
Published electronically: October 24, 2018
Additional Notes: This research was supported in part by NSA grant H98230-13-1-0237.
Article copyright: © Copyright 2018 American Mathematical Society