Kac-Moody Algebras, the Monstrous Moonshine, Jacobi Forms and Infinite Products

Abstract

In this article, we discuss the relation between Kac-Moody algebras, the monstrous moonshine, Jacobi forms and infinite products. We also review Borcherds' solution of the Moonshine Conjecture and his work of constructing automorphic forms on the orthogonal group which can be written as infinite products.

78 pages I added two more Dynkin diagrams in page 7. I corrected several typos

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