Automorphic forms, fake monster algebras, and hyperbolic reflection groups (Q5957474)

Two families of automorphic forms related to twisted fake monster algebras are constructed. This gives a new prove of their denominator identities and shows that they define automorphic forms of singular weight. It is derived analogous results for twisted fake monster superalgebras. In addition the author gets new infinite product identities which are the denominator identities of generalized Kac-Moody superalgebras. He also describes the reflection groups of the root lattices of the generalized Kac-Moody algebras. In the bosonic case they are related to automorphic forms. In the super case Vinberg's algorithm is used to determine their fundamental domains.