L-packets over strong real forms
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- by N. Arancibia Robert and P. Mezo
- Represent. Theory 28 (2024), 20-48
- DOI: https://doi.org/10.1090/ert/667
- Published electronically: January 5, 2024
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Abstract:
Langlands [On the classification of irreducible representations of real algebraic groups, Math. Surveys Monogr., vol. 31, Amer. Math. Soc., Providence, RI, 1989, pp. 101–170] defined $L$-packets for real reductive groups. In order to refine the local Langlands correspondence, Adams-Barbasch-Vogan [The Langlands classification and irreducible characters for real reductive groups, Progress in Mathematics, vol. 104, Birkhäuser Boston, Inc., Boston, MA, 1992] combined L-packets over all real forms belonging to an inner class. In the tempered setting, using different methods, Kaletha [Ann. of Math. (2) 184 (2016), pp. 559–632] also defines such combined L-packets with a refinement to the local Langlands correspondence. We prove that the tempered L-packets of Adams-Barbasch-Vogan and Kaletha are the same and are parameterized identically.References
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Bibliographic Information
- N. Arancibia Robert
- Affiliation: Département de Mathématiques, CY Cergy Paris Université, Cergy, France
- Email: nicolas.arancibia-robert@cyu.fr
- P. Mezo
- Affiliation: The School of Mathematics and Statistics, Carleton University, Ottawa, Canada
- MR Author ID: 685639
- Email: mezo@math.carleton.ca
- Received by editor(s): September 23, 2022
- Received by editor(s) in revised form: September 7, 2023, and October 19, 2023
- Published electronically: January 5, 2024
- Additional Notes: Partially supported by NSERC grant RGPIN-06361, and CY Advanced Studies Institute
- © Copyright 2024 American Mathematical Society
- Journal: Represent. Theory 28 (2024), 20-48
- MSC (2020): Primary 22E47
- DOI: https://doi.org/10.1090/ert/667
- MathSciNet review: 4685815