On the generic local Langlands correspondence for $GSpin$ groups
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- by Volker Heiermann and Yeansu Kim PDF
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Abstract:
In the case of split $GSpin$ groups, we prove an equality of $L$-functions between automorphic local $L$-functions defined by the Langlands-Shahidi method and local Artin $L$-functions. Our method of proof is based on previous results of the first author which allow us to reduce the problem to supercuspidal representations of Levi subgroups of $GSpin$, by constructing Langlands parameters for general generic irreducible admissible representations of $GSpin$ from the one for generic irreducible supercuspidal representations of its Levi subgroups.References
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Additional Information
- Volker Heiermann
- Affiliation: Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
- MR Author ID: 351327
- Email: volker.heiermann@univ-amu.fr
- Yeansu Kim
- Affiliation: Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242 – and – Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
- Address at time of publication: Department of Mathematics Education, Chonnam National University, 77, Yongbong-ro, Buk-gu, Gwangju, 61186, Korea
- MR Author ID: 1094118
- ORCID: 0000-0001-9427-6136
- Email: ykim@jnu.ac.kr
- Received by editor(s): February 3, 2014
- Received by editor(s) in revised form: July 15, 2015
- Published electronically: December 22, 2016
- Additional Notes: The first author has benefitted from the help of the Agence Nationale de la Recherche with reference ANR-08-BLAN-0259-02.
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 4275-4291
- MSC (2010): Primary 11F70, 11S37, 22E50
- DOI: https://doi.org/10.1090/tran/6791
- MathSciNet review: 3624409