# Some results on Bessel functionals for GSp(4)

### Brooks Roberts

Department of Mathematics Department of Mathematics University of Idaho University of Oklahoma Moscow, ID 83844-1103 Norman, OK 73019-3103 USA USA### Ralf Schmidt

Department of Mathematics Department of Mathematics University of Idaho University of Oklahoma Moscow, ID 83844-1103 Norman, OK 73019-3103 USA USA

## Abstract

We prove that every irreducible, admissible representation $\pi$ of $\GSp(4,F)$, 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.

## Cite this article

Brooks Roberts, Ralf Schmidt, Some results on Bessel functionals for GSp(4). Doc. Math. 21 (2016), pp. 467–553

DOI 10.4171/DM/539