Kac-Moody algebras, the Monstrous Moonshine, Jacobi forms and infinite products

초록

This is an excellent survey article about the recent impressive works of R. E. Borcherds(the Fields medalist of 1998). The results of Borcherds presented in this article are (i) construction of the Monster Lie algebra, (ii) proof of the Moonshine conjectures, (iii) construction of automorphic forms on the orthogonal group $O_{s+2,2}(\mathbb{R})$, (iv) infinite product representations of meromorphic modular forms, and (v) construction of Jacobi forms. In the final remarks, open problems are formulated. Reviewed by Noriko Yui(Kingston, Canada); 98b:11042(Math. Review; American Math. Soc.) 이 논문은 R. E. Borcherds의 논문 "Automorphic forms and Lie algebras"과 "What is moonshine?"에 인용되었음