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Representation Theory

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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
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

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