Some results on Bessel functionals for GSp(4)

2014/12/31 by Brooks Roberts, Roberts, Brooks, Ralf Schmidt +1 · 1 citation
Materials Science · Mathematics · #11F30 (Secondary) #11F46 #11F70 #22E50 (Primary) #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Lanthanide and Transition Metal Complexes #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1501.00221

openalex publication_date 2014/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every irreducible, admissible representation of GSp(4,F), where F is a non-archimedean local field of characteristic zero, admits a Bessel functional, provided the representation is not one-dimensional. Given such a representation, we explicitly determine the set of all split Bessel functionals admitted by the representation, and prove that these functionals are unique. If the representation is not supercuspidal, or in an L-packet with a non-supercuspidal representation, we explicitly determine the set of all Bessel functionals admitted by the representation, and prove that these functionals are unique.

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• Euler systems for GSp(4) over imaginary quadratic fields

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