Local Shalika models and functoriality

Dihua Jiang; Chufeng Nien; Yujun Qin

doi:10.1007/s00229-008-0200-0

Local Shalika models and functoriality

Dihua Jiang
, Chufeng Nien
, Yujun Qin

School of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We prove, over a p-adic local field F, that an irreducible supercuspidal representation of GL_2n(F) is a local Langlands functorial transfer from SO_2n+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.

Original language	English (US)
Pages (from-to)	187-217
Number of pages	31
Journal	Manuscripta Mathematica
Volume	127
Issue number	2
DOIs	https://doi.org/10.1007/s00229-008-0200-0
State	Published - Oct 2008

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10.1007/s00229-008-0200-0

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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.",

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T1 - Local Shalika models and functoriality

AU - Jiang, Dihua

AU - Nien, Chufeng

AU - Qin, Yujun

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N2 - 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.

AB - 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.

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Local Shalika models and functoriality

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