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

Marcela Hanzer

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 symple…