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

Jantzen, Chris

doi:10.1090/ert/519

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

Represent. Theory 22 (2018), 160-201

DOI: https://doi.org/10.1090/ert/519

Published electronically: October 24, 2018

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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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