Contragredient representations and characterizing the local Langlands correspondence
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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,ℝ).
Date issued
2016-06Department
Massachusetts Institute of Technology. Department of MathematicsJournal
American Journal of Mathematics
Publisher
Johns Hopkins University Press
Citation
Adams, Jeffrey and David A. Vogan. “Contragredient Representations and Characterizing the Local Langlands Correspondence.” American Journal of Mathematics 138, 3 (June 2016): 657–682 © 2016 Johns Hopkins University Press
Version: Final published version
ISSN
1080-6377
0002-9327