Another product for a Borcherds form

摘要

Among the remarkable properties of the meromorphic modular forms on the hermitian symmetric domain D associated to a rational quadratic space V, (,) of signature (n,2) constructed by Borcherds are product formulas,each valid in a neighborhood of a point boundary component. In this paper,under the assumption that V, (,), admits 2-dimensional rational isotropic subspaces,some new product formulas for these modular forms are described,each valid in the neighborhood of a 1-dimensional boundary component of D. The products involve Jacobi theta functions and eta functions and arise by a calculation of the Fourier expansion of the regularized theta lift along the unipotent radical of the maximal parabolic subgroup of SO (V) stabilizing an isotropic 2-plane.