On the generic local Langlands correspondence for 𝐺𝑆𝑝𝑖𝑛 groups

Abstract

In the case of split G S p i n GSpin groups, we prove an equality of L L -functions between automorphic local L L -functions defined by the Langlands-Shahidi method and local Artin L 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 G S p i n GSpin , by constructing Langlands parameters for general generic irreducible admissible representations of G S p i n GSpin from the one for generic irreducible supercuspidal representations of its Levi subgroups.