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On the generic local Langlands correspondence for $ GSpin$ groups


Authors: Volker Heiermann and Yeansu Kim
Journal: Trans. Amer. Math. Soc. 369 (2017), 4275-4291
MSC (2010): Primary 11F70, 11S37, 22E50
DOI: https://doi.org/10.1090/tran/6791
Published electronically: December 22, 2016
MathSciNet review: 3624409
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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.


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Additional Information

Volker Heiermann
Affiliation: Aix Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France
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
Email: ykim@jnu.ac.kr

DOI: https://doi.org/10.1090/tran/6791
Keywords: Generic Arthur packet conjecture, local Langlands correspondence, Langlands-Shahidi method
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.
Article copyright: © Copyright 2016 American Mathematical Society