Generalized Shalika model on SO_(4n)(F), symplectic linear model on Sp_(4n)(F) and theta correspondence
classification
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math.NT
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mathrmmodelgeneralizedlinearshalikasymplecticthetaadmissible
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We show that if an irreducible admissible representation of $\mathrm{SO}_{4n}(F)$ has a generalized Shalika model, then its small theta lift to $\mathrm{Sp}_{4n}(F)$ has the symplectic linear model, thus answering a question posed by D. Jiang. Here $F$ is a non-archimedean field of characteristic zero.
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