Generalized moonshine, II: Borcherds products

Generalized Moonshine Ii: Borcherds Products

The goal of this paper is to construct infinite dimensional Lie algebras using infinite product identities, and to use these Lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex algebras and Lie algebras. The Lie algebras that we construct conjecturally appear in an orbifold conformal field theory with symmetries given by the monster ...

Borcherds’ proof of the moonshine conjecture

These CSG notes contain a condensed account of a talk by V. Nikulin in the London algebra Colloquium on 24 May 2001. None of the content is original to me: it is provided simply as a service for those who missed Nikulin’s talks. I have relied mainly on my notes from the lectures, So any errors are the product of the note-taking and are not to be attributed to the content of the lectures. 1 The ...

Notes on Borcherds Products

These are the notes for a short course on Borcherds Products held in Aachen on 1st2nd August 2012. The lectures are intended for someone who does not know what a Borcherds product is, but does know what a modular form is. In preparing these notes I’ve used the following sources: [1, 2, 3, 4, 5]. All the correct statements in these notes are taken from those sources, and all the mistakes are my ...

Local Borcherds products

Lattices with many Borcherds products

We prove that there are only finitely many isometry classes of even lattices L of signature (2, n) for which the space of cusp forms of weight 1 + n/2 for the Weil representation of the discriminant group of L is trivial. We compute the list of these lattices. They have the property that every Heegner divisor for the orthogonal group of L can be realized as the divisor of a Borcherds product. W...