Contragredient representations over local fields of positive characteristic

Li, Wen-Wei

doi:10.2140/ant.2019.13.1197

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Contragredient representations over local fields of positive characteristic

Wen-Wei Li

Vol. 13 (2019), No. 5, 1197–1242

DOI: 10.2140/ant.2019.13.1197

Abstract

It was conjectured bsy Adams, Vogan and Prasad that under the local Langlands correspondence, the $L$ -parameter of the contragredient representation equals that of the original representation composed with the Chevalley involution of the $L$ -group. We verify a variant of their prediction for all connected reductive groups over local fields of positive characteristic, in terms of the local Langlands parametrization of A. Genestier and V. Lafforgue. We deduce this from a global result for cuspidal automorphic representations over function fields, which is in turn based on a description of the transposes of Lafforgue’s excursion operators.

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Keywords

contragredient representation, function field, local Langlands conjecture

Mathematical Subject Classification 2010

Primary: 11F70

Secondary: 11R58, 22E55

Milestones

Received: 16 October 2018

Revised: 9 January 2019

Accepted: 10 March 2019

Published: 12 July 2019

Authors

Wen-Wei Li
Beijing International Center for Mathematical Research Peking University Beijing China

Vol. 13, No. 5, 2019