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

广义 Kac-Moody 代数、自守形式和双曲反射群

• 批准号: 5236382
• 负责人: Professor Dr. Nils R. Scheithauer
• 金额: --
• 依托单位: Arbeitsgruppe Algebra
• 依托单位国家: 德国
• 项目类别: Independent Junior Research Groups
• 财政年份: 2000
• 资助国家: 德国
• 起止时间: 1999-12-31 至 2007-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5236382?language=en
• 关键词: Generalized; Kac; Moody; algebras; automorphic

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.

本项目分为3个部分：1.设计方案；伪怪物超代数的扭曲分母恒等式的计算及其在3种情况下的应用：a)广义Kac-Moody超代数新实例的构造及其单根和根重的显式描述。b)新的自同构形式的构造及其积展开式的描述。c)研究某些扭曲分母函数是否在簇的模空间上定义函数。证明在环面上运动的N=2手性超弦的物理状态形成了2.3阶广义Kac-Moody超代数。用高维顶点代数描述闭弦和杂弦，并研究由此产生的对称性。