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

TL;DR

This paper establishes the uniqueness and existence criteria for Bessel models in lowest and highest weight representations of GSp(4,R) and Sp(4,R), providing explicit formulas and applications to global L-functions.

Contribution

It introduces new criteria and explicit formulas for Bessel models in specific representations of GSp(4,R), including applications to L-functions.

Findings

Criteria for existence of Bessel models established

Explicit formulas for Bessel functions derived

Application to integral representations of L-functions

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.