The local converse theorem for SO(2n+1) and applications

• 成果类型: Article
• 署名作者: Jiang, DH; Soudry, D
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2003.157.743
• 发表日期: 2003
• 页码: 743-806
• 关键词: multiplicity one theorem; induced representations; gamma-factors; gl(n); conjecture; MODULES; PROOF

摘要

In this paper we characterize irreducible generic representations of SO2n+1 (k) (where k is a p-adic field) by means of twisted local gamma factors (the Local Converse Theorem). As applications, we prove that two irreducible generic cuspidal automorphic representations of SO2n+1(A) (where A is the ring of adeles of a number field) are equivalent if their local components are equivalent at almost all local places (the Rigidity Theorem); and prove the Local Langlands Reciprocity Conjecture for generic supercuspidal representations of SO2n+1(k).