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

Dihua Jiang·David Soudry
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Abstract

In this paper we characterize irreducible generic representations of $\SO_{2n+1}(k)$ 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 $\SO_{2n+1}({\Bbb A})$ (where ${\Bbb A}$ 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 $\SO_{2n+1}(k)$.

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Dihua Jiang, David Soudry. 2004-02-16. The local converse theorem for SO(2n+1) and applications. https://arxiv.org/abs/math/0402265

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