Orbifold映射空间的无穷乘积分解
Infinite Product Decomposition of Orbifold Mapping Spaces
摘要：
物理学家们证明了对称轨道的轨道椭圆型的母函数可以写成一个无穷乘积。我们证明了在更一般的框架下，在这个无穷乘积公式背后存在空间水平上的几何因式分解，其中无穷乘积中的因子对应于所涉及流形的连通有限覆盖空间的同构类.从这个公式中，出现了函子的几何Hecke算子的概念。我们表明，这些Hecke运营商确实满足通常的身份Hecke运营商的情况下，2维环面。
英文摘要：
Physicists showed that the generating function of orbifold elliptic genera of symmetric orbifolds can be written as an infinite product. We show that there exists a geometric factorization on space level behind this infinite product formula in much more general framework, where factors in the infinite product correspond to isomorphism classes of connected finite covering spaces of manifolds involved. From this formula, a concept of geometric Hecke operators for functors emerges. We show that these Hecke operators indeed satisfy the usual identity of Hecke operators for the case of 2-dimensional tori.
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