The local converse theorem for quasi-split O_2n and SO_2n

2023/01/30 by Haan, Jaeho, Kim, Yeansu, Kwon, Sanghoon
#FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2301.12693

Abstract

Let F be a non-archimedean local field of characteristic not equal to 2. In this paper, we prove the local converse theorem for quasi-split Ø_2n(F) and \SO_2n(F), via the description of the local theta correspondence between Ø_2n(F) and \Sp_2n(F). More precisely, as a main step, we explicitly describe the precise behavior of the γ-factors under the correspondence. Furthermore, we apply our results to prove the weak rigidity theorems for irreducible generic cuspidal automorphic representations of Ø_2n(\A) and \SO_2n(\mathbbA), respectively, where \A is a ring of adele of a global number field L.

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