Symmetries for automorphic forms on orthogonal groups (joint work with Bernhard Heim)

Borcherds lifts on $G=O(2,n+2)$ are meromorphic automorphic forms
whose divisors are Heegner divisors. In this talk, we discuss on
holomorphic automorphic forms
on  $G$ satisfying certain symmetries. We show that, with an additional
assumption,
these forms are Borcherds lifts. In the cases of $n=0$ and $n=1$, we can
remove this
additional condition and hence Borcherds lifts are characterized by the
symmetries.