The theta correspondence is a correspondence between automorphic forms over two groups.

We can understand this theory from local to global: Due to Howe,given two p-adic groups G and H and a representation of G, we can obtain an associated representation of H. Using the theory of automorphic forms we translate this local statement into an automorphic statement. I will introduce the Borcherds product, an specific example of theta lift for orthogonal Shimura varieties.