Hurwitz配分函数的可积性。II。割并算子与WDVV方程的乘法
Integrability properties of Hurwitz partition functions. II. Multiplication of cut-and-join operators and WDVV equations
摘要：
拓扑理论中的相关子由交换结合代数（CAA）中的算子积的线性形式的值给出。作为推论，拓扑理论的配分函数总是满足广义WDVV方程。我们考虑赫尔维茨配分函数，以这种方式与CAA的切割和连接运营商。普通的Hurwitz数为一个给定数量的表中的覆盖提供平凡的（指数和）解决方案的WDVV方程，有限数量的时间变量。arXiv：0904.4227中的广义Hurwitz数提供了无限次的非平凡解。这种类型的最简单的解与一个由伸缩算子tr X（d/dX）生成的子环相关联。
英文摘要：
Correlators in topological theories are given by the values of a linear form on the products of operators from a commutative associative algebra (CAA). As a corollary, partition functions of topological theory always satisfy the generalized WDVV equations. We consider the Hurwitz partition functions, associated in this way with the CAA of cut-and-join operators. The ordinary Hurwitz numbers for a given number of sheets in the covering provide trivial (sums of exponentials) solutions to the WDVV equations, with finite number of time-variables. The generalized Hurwitz numbers from arXiv:0904.4227 provide a non-trivial solution with infinite number of times. The simplest solution of this type is associated with a subring, generated by the dilatation operators tr X(d/dX).
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