Generalized Shalika model on ${\mathrm{SO}}_{4n}(F),$ symplectic linear model on ${\mathrm{Sp}}_{4n}(F)$ and theta correspondence

Abstract

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.

References in corpus (1)

• Restrictions of representations of classical groups: examples