Kac-Moody Algebras, the Monstrous Moonshine, Jacobi Forms and Infinite Products
Jae-Hyun Yang
TL;DR
This paper explores the connections between Kac-Moody algebras, monstrous moonshine, Jacobi forms, and infinite products, highlighting Borcherds' contributions to automorphic forms and the Moonshine Conjecture.
Contribution
It reviews Borcherds' construction of automorphic forms as infinite products and his solution to the Moonshine Conjecture, linking algebraic and automorphic structures.
Findings
Borcherds' automorphic forms can be expressed as infinite products.
The paper clarifies the relationship between Kac-Moody algebras and moonshine phenomena.
It provides a comprehensive review of the mathematical structures connecting these areas.
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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory