  It is conjectured by 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 parameterization of Genestier-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 V. Lafforgue's
excursion operators.
