Abstract

Automorphic products are modular forms with infinite product expansions and special zeros. For example, the denominator of the Weyl-Kac character formula of any affine Lie algebra defines an automorphic product of singular (i.e. minimal) weight as a Jacobi form. In this talk, we discuss automorphic products of singular weight on orthogonal groups O(n, 2). This type of modular form is often the denominator of some Borcherds-Kac-Moody Lie algebra, and is related to vertex operator algebras. It was conjectured that there are only finitely many such modular forms. We present some results on the classification and construction of these exceptional modular forms. This talk is based on joint work with Brandon Williams.