论文标题
加权的Hurwitz数字，$τ$ - 功能和矩阵积分
Weighted Hurwitz numbers, $τ$-functions and matrix integrals
论文作者
论文摘要
跨越Sato Grassmannian元素的基础元素对应于KP $τ$功能，该功能是为合理加权的Hurwitz编号生成功能，被证明是Meijer $ G $ - 功能。使用其Mellin-Barnes积分表示，在外部耦合矩阵的痕量不变式上评估$τ$函数，表示为矩阵积分。使用$γ$函数的无限产品的Mellin-Barnes积分转换，为KP $τ$函数提供了类似的矩阵积分表示，该表示是为量子加权Hurwitz编号生成函数的。
The basis elements spanning the Sato Grassmannian element corresponding to the KP $τ$-function that serves as generating function for rationally weighted Hurwitz numbers are shown to be Meijer $G$-functions. Using their Mellin-Barnes integral representation the $τ$-function, evaluated at the trace invariants of an externally coupled matrix, is expressed as a matrix integral. Using the Mellin-Barnes integral transform of an infinite product of $Γ$ functions, a similar matrix integral representation is given for the KP $τ$-function that serves as generating function for quantum weighted Hurwitz numbers.
