DOCUMENTA MATHEMATICA, Vol. 21 (2016), 467-553

Brooks Roberts and Ralf Schmidt

Some Results on Bessel Functionals for GSp(4)

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.

2010 Mathematics Subject Classification: Primary 11F70 and 22E50

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