#### Vol. 13, No. 5, 2019

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Contragredient representations over local fields of positive characteristic

### Wen-Wei Li

Vol. 13 (2019), No. 5, 1197–1242
##### 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.

##### 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