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引用次数: 0
摘要
根据 Cartan 对紧凑对称空间的分类,我们定义了两种类型的威滕 zeta 函数。为了构造 I 型 zeta 函数,我们使用米格达尔-维滕方法计算了具有破规对称性的 2d YM 理论的分割函数。我们证明,对于秩一对称空间,整数参数的 I 型函数值的生成数列可以用黎曼zeta函数的生成数列来定义。
We define two types of Witten’s zeta functions according to Cartan’s classification of compact symmetric spaces. The type II is the original Witten zeta function constructed by means of irreducible representations of the simple compact Lie group U. The type I Witten zeta functions, we introduce here, are related to the irreducible spherical representations of U. They arise in the harmonic analysis on compact symmetric spaces of the form U/K, where K is the maximal subgroup of U. To construct the type I zeta function we calculate the partition functions of 2d YM theory with broken gauge symmetry using the Migdal–Witten approach. We prove that for the rank one symmetric spaces the generating series for the values of the type I functions with integer arguments can be defined in terms of the generating series of the Riemann zeta-function.
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