Generalized Kac-Moody algebras, automorphic forms and hyperbolic reflection groups

本项目分为三个部分：1.伪Monster超代数的扭分母恒等式的计算及其在3种情况下的应用：a)构造广义Kac-Moody超代数的新实例，并显式刻画它们的单根和根重；b)构造新的自同构形式并刻画它们的乘积展开式；c)考察某些扭曲分母函数是否定义了变元模空间上的函数。证明了在环面上运动的手征N=2超弦的物理态构成了一个秩为2.3的广义Kac-Moody超代数。用高维顶点代数描述闭弦和杂弦，并研究这里产生的对称性。

The project is divided into 3 parts:1. Calculation of twisted denominator identities of the fake monster superalgebra and their application in 3 cases:a) Construction of new examples of generalized Kac-Moody superalgebras and explicit description of their simple roots and root multiplicities.b) Construction of new automorphic forms and description of their product expansions.c) Investigation whether some of the twisted denominator functions define functions on moduli spaces of varieties.2. Prove that the physical states of a chiral N=2 superstring moving on a torus form a generalized Kac-Moody superalgebra of rank 2.3. Describe closed and heterotic strings by higher dimensional vertex algebras and study the symmetries arising here.