The Weil Representation of and Some Applications
The Weil Representation of and Some Applications
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的 Weil 表示和一些应用
DOI：
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发表时间：
2009
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通讯作者：
Nils R. Scheithauer
中科院分区：
文献类型：
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作者：
Nils R. Scheithauer
偶数秩的正定偶数格的θ函数在该格的判别式的群代数上生成的表示。这种表示可以追溯到Jacobi，称为Weil表示。我们推导出一个明确的公式的作用格的亏格。这推广了Schoeneberg和Weil的经典结果。我们使用该公式计算从Γ 0（N）上的标值模形式到Weil表示的模形式的提升。我们还表明，Mathieu群M 23的元素自然对应于反射自守产品的奇异重量，我们构建了三个广义卡茨-穆迪超代数表示超对称超弦的尺寸10，6，和4。
The theta function of a positive definite even lattice of even rank generates a representation of on the group algebra of the discriminant form of the lattice. This representation goes back to Jacobi and is called Weil representation. We derive an explicit formula for the action in terms of the genus of the lattice. This generalizes classical results of Schoeneberg and Weil. We use the formula to calculate the lift from scalar-valued modular forms on Γ 0 (N) to modular forms for the Weil representation. We also show that the elements of the Mathieu group M 23 correspond naturally to reflective automorphic products of singular weight, and we construct three generalized Kac-Moody superalgebras representing supersymmetric superstrings in dimensions 10, 6, and 4.