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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Jiang, D., Nien, C. & Qin, Y. Local Shalika models and functoriality. manuscripta math. 127, 187–217 (2008). https://doi.org/10.1007/s00229-008-0200-0
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DOI: https://doi.org/10.1007/s00229-008-0200-0