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 ${\text{U}}_{E/F}(2,2)$ 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 ${\text{Sp}}_4(F)$ and ${\widetilde{\text{Sp}}}_4(F)$ if the residue characteristic of $F$ is odd.

version 2, 24 pages

References in corpus (3)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Towards the Jacquet Conjecture on the Local Converse Problem for $p$-adic ${\mathrm{GL}}_n$
• On the Local Converse Theorem for p-adic GLn

Cited by in corpus (3)

• Bessel functions and local converse conjecture of Jacquet
• On the Local Converse Theorem for p-adic GLn
• On the local converse theorem and the descent theorem in families