On the generic local Langlands correspondence for 𝐺𝑆𝑝𝑖𝑛 groups

Heiermann, Volker; Kim, Yeansu

doi:10.1090/tran/6791

On the generic local Langlands correspondence for $GSpin$ groups
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by Volker Heiermann and Yeansu Kim PDF

Trans. Amer. Math. Soc. 369 (2017), 4275-4291 Request permission

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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