Theta function transformation formulas and the Weil representation (Q1059102)

This paper establishes a new connection between the Weil representation of the metaplectic cover of Sp(2,\({\mathbb{R}})\) and the corresponding Siegel theta functions on the Siegel half-space. The Weil representation is equipped with a linear functional which gives rise in a standard way to the theta functions. The author reverses this process and represents the linear functional as a limit of functionals formed by integrating against the theta function. From this representation he is able to deduce the invariance properties of the functional from those of the theta function.