Theta function transformation formulas and the Weil representation
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.
explicit determination of eigth root of unity
metaplectic cover of Sp(2,\({\mathbb{R}})\)
scientific article; zbMATH DE number 3902748