Vol. 7, No. 10, 2013

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Genericity and contragredience in the local Langlands correspondence

Tasho Kaletha

Vol. 7 (2013), No. 10, 2447–2474
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.

Keywords
local Langlands correspondence, contragredient, generic, Whittaker data, $L$-packet, classical group
Mathematical Subject Classification 2010
Primary: 11S37
Secondary: 22E50
Milestones
Received: 14 July 2012
Revised: 25 January 2013
Accepted: 26 April 2013
Published: 18 January 2014
Authors
Tasho Kaletha
Department of Mathematics
Princeton University
Fine Hall, Washington Road
Princeton, NJ 08544
United States