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Contragredient representations and characterizing the local Langlands correspondence
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 138, Number 3, June 2016
- pp. 657-682
- 10.1353/ajm.2016.0024
- Article
- Additional Information
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We consider the question: what is the contragredient in terms of
L-homomorphisms? We conjecture that it corresponds to the Chevalley
automorphism of the L-group, and prove this in the case of real groups.
The proof uses a characterization of the local Langlands correspondence
over $R$. We also consider the related notion of Hermitian dual, in the
case of GL$(n,{\Bbb R})$.