Invariants for the Weil representation and modular units for orthogonal groups of signature (2,2)

Abstract

We show that the space of invariants for the Weil representation for discriminant groups which contain self-dual isotropic subgroups is spanned by the characteristic functions of the self-dual isotropic subgroups. As an application, we construct modular units for certain orthogonal groups in signature (2,2) using Borcherds products.