A Characterization of Holomorphic Borcherds Lifts by Symmetries

In this paper, we show that, in the holomorphic automorphic case, the Borcherds lifts on the orthogonal group O(2,n + 2) are characterized by certain symmetries and describe the inverse of the Borcherds lifting in terms of Fourier–Jacobi expansion. We also give a characterization of the modular polynomials by certain symmetries.