Bessel models for lowest weight representations of GSp(4,R)

2008/09/02 by Ameya Pitale, Pitale, Ameya, Ralf Schmidt +1 · 7 citations
Mathematics · #11F67 (Secondary) #11F70 (Primary) 11F46 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Mathematical Analysis and Transform Methods #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0809.0482

openalex publication_date 2008/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove uniqueness and give precise criteria for existence of split and non-split Bessel models for a class of lowest and highest weight representations of the groups GSp(4,R) and Sp(4,R) including all holomorphic and anti-holomorphic discrete series representations. Explicit formulas for the resulting Bessel functions are obtained by solving systems of differential equations. The formulas are applied to derive an integral representation for a global L-function on GSp(4)xGL(2) involving a vector-valued Siegel modular form of degree 2.

Cited by

• Integral representation for L-functions for GSp(4) x GL(2), II
• Transfer of Siegel cusp forms of degree 2
• Pullbacks of Eisenstein series from GU(3,3) and critical L-values for GSp(4) X GL(2)
• Steinberg representation of GSp(4): Bessel models and integral representation of L-functions
• On the degree five L-function for GSp(4)
• Local and global Maass relations (expanded version)
• Bessel periods and anticyclotomic p-adic spinor L-functions

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