Algebra & Number Theory

Genericity and contragredience in the local Langlands correspondence

Tasho Kaletha

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Abstract

Adams, Vogan, and D. Prasad have given conjectural formulas for the behavior of the local Langlands correspondence with respect to taking the contragredient of a representation. We prove these conjectures for tempered representations of quasisplit real K-groups and quasisplit p-adic classical groups (in the sense of Arthur). We also prove a formula for the behavior of the local Langlands correspondence for these groups with respect to changes of the Whittaker data.

Article information

Source
Algebra Number Theory, Volume 7, Number 10 (2013), 2447-2474.

Dates
Received: 14 July 2012
Revised: 25 January 2013
Accepted: 26 April 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513730113

Digital Object Identifier
doi:10.2140/ant.2013.7.2447

Mathematical Reviews number (MathSciNet)
MR3194648

Zentralblatt MATH identifier
1371.11148

Subjects
Primary: 11S37: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]
Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Keywords
local Langlands correspondence contragredient generic Whittaker data $L$-packet classical group

Citation

Kaletha, Tasho. Genericity and contragredience in the local Langlands correspondence. Algebra Number Theory 7 (2013), no. 10, 2447--2474. doi:10.2140/ant.2013.7.2447. https://projecteuclid.org/euclid.ant/1513730113


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