SYMMETRIES FOR BORCHERDS LIFTS ON HILBERT MODULAR GROUPS AND HIRZEBRUCH–ZAGIER DIVISORS

Abstract

We show certain symmetries for Borcherds lifts on the Hilbert modular group over a real quadratic field. We give two different proofs, the one analytic and the other arithmetic. The latter proof yields an explicit description of the action of Hecke operators on Borcherds lifts.