论文标题
假怪物代数和奇异的Borcherds产品
The fake monster algebra and singular Borcherds products
论文作者
论文摘要
在本文中，我们考虑了Borcherds在1995年提出的自动形成产品理论和广义的kac--moody代数中的几个问题。我们表明，假怪物代数的分母定义了在最大效果上定义独特的霍明型骨质borcherds产品。我们对质量水平的奇异重量的对称性全态鲍尔切德（Borcherds）产物进行完整分类。最终，我们证明了假怪物代数的所有扭曲分母的身份都出现，因为在某个尖端上，象牙色的鲍尔切尔德产品的傅立叶膨胀。这些证明依赖于在$ u（n）\ oplus u \ oplus l $和某些jacobi级别的级别$ n $的单元的模块化表单之间的标识。
In this paper we consider several problems in the theory of automorphic products and generalized Kac--Moody algebras proposed by Borcherds in 1995. We show that the denominator of the fake monster algebra defines the unique holomorphic Borcherds product of singular weight on a maximal lattice. We give a full classification of symmetric holomorphic Borcherds products of singular weight on lattices of prime level. Finally we prove that all twisted denominator identities of the fake monster algebra arise as the Fourier expansions of Borcherds products of singular weight at a certain cusp. The proofs rely on an identification between modular forms for the Weil representation attached to lattices of type $U(N)\oplus U \oplus L$ and certain tuples of Jacobi forms of level $N$.
