S ep 2 00 8 Bessel models for lowest weight representations of GSp ( 4 , R )

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)×GL(2) involving a vector-valued Siegel modular form of degree 2.