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manuscripta mathematica

, Volume 127, Issue 2, pp 187–217 | Cite as

Local Shalika models and functoriality

  • Dihua JiangEmail author
  • Chufeng Nien
  • Yujun Qin
Article

Abstract

We prove, over a p-adic local field F, that an irreducible supercuspidal representation of GL2n (F) is a local Langlands functorial transfer from SO2n+1(F) if and only if it has a nonzero Shalika model (Corollary 5.2, Proposition 5.4 and Theorem 5.5). Based on this, we verify (Sect. 6) in our cases a conjecture of Jacquet and Martin, a conjecture of Kim, and a conjecture of Speh in the theory of automorphic forms.

Mathematics Subject Classification (2000)

Primary 11F70 22E50 Secondary 11F85 22E55 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of MathematicsNational Cheng Kung UniversityTainanTaiwan
  3. 3.Department of MathematicsEast China Normal UniversityShanghaiPeople’s Republic of China

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