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

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.

contragredient representation, function field, local Langlands conjecture
Mathematical Subject Classification 2010
Primary: 11F70
Secondary: 11R58, 22E55
Received: 16 October 2018
Revised: 9 January 2019
Accepted: 10 March 2019
Published: 12 July 2019
Wen-Wei Li
Beijing International Center for Mathematical Research
Peking University