Vol. 7, No. 10, 2013

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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
Primary: 11S37
Secondary: 22E50