Invariants for the Weil representation and Modular Units for Orthogonal Groups of Signature (2,2)
arXiv:2108.08107 · doi:10.1016/j.jnt.2023.03.002
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 orthogonal groups in signature (2,2) using Borcherds products.
24 pages, final version, to appear in Journal of Number Theory