Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras
Siegel automorphic form corrections of some Lorentzian Kac-Moody Lie algebras
复制标题
一些洛伦兹 Kac-Moody 李代数的 Siegel 自守形式修正
DOI：
10.1353/ajm.1997.0002
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发表时间：
1995
影响因子：
1.7
通讯作者：
V. Nikulin
中科院分区：
文献类型：
--
作者：
V. Gritsenko;V. Nikulin
对于两个秩为3的椭圆型Lorentzian Kac-Moody代数，给出了无奇真实的单根的广义Lorentzian Kac-Moody超代数的自守形式修正，并计算了它们的单根和任意根的重数.这些Kac-Moody代数由秩为3的双曲对称化广义Cartan矩阵[inline-graphic xmlns：xlink=”http://www.w3.org/1999/xlink“xlink：href=“01 i”/]定义。这两个代数都有椭圆型（即，它们的Weyl群在相应的双曲空间中具有有限体积的基本多面体）并且具有格Weyl向量。修正自守形式是Siegel模形式。对应于G 1的形式是权为5的经典Siegel尖点形式，它是10个偶数θ-常数的乘积。特别是，我们找到了一个无限的产品公式，这个模块的形式。
We find automorphic form corrections which are generalized Lorentzian Kac-Moody superalgebras without odd real simple roots for two elliptic Lorentzian Kac-Moody algebras of rank 3 with a lattice Weyl vector, and calculate multiplicities of their simple and arbitrary roots. These Kac-Moody algebras are defined by hyperbolic symmetrized generalized Cartan matrices [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] of rank 3. Both these algebras have elliptic type (i.e., their Weyl groups have fundamental polyhedra of finite volume in corresponding hyperbolic spaces) and have a lattice Weyl vector. The correcting automorphic forms are Siegel modular forms. The form corresponding to G 1 is the classical Siegel cusp form of weight 5 which is the product of ten even theta-constants. In particular we find an infinite product formula for this modular form.