Some results on Bessel functionals for GSp(4)

Abstract

We prove that every irreducible, admissible representation $\pi$ of $\mathrm{GSp}(4,F)$, where $F$ is a non-archimedean local field of characteristic zero, admits a Bessel functional, provided $\pi$ is not one-dimensional. If $\pi$ is not supercuspidal, we explicitly determine the set of all Bessel functionals admitted by $\pi$, and prove that Bessel functionals of a fixed type are unique. If $\pi$ is supercuspidal, we do the same for all split Bessel functionals.