A local converse Theorem for U(2,2)

Abstract

Let $F$ be a $p$-adic field and $E/F$ be a quadratic extension. In this paper, we prove the local converse theorem for generic representations of $\textrm{U}_{E/F}(2,2)$ if $E/F$ is unramified or the residue characteristic of $F$ is odd. Our method is purely local and analytic, and the same method also gives the local converse theorem for $\textrm{Sp}_4(F)$ and $\widetilde {\textrm{Sp}}_4(F)$ if the residue characteristic of $F$ is odd.