Deligne-Simpson问题与Hurwit计数问题的关系  

On relationship of the Deligre-Simpson problem and the Harwitz enumeration problem

作　　者：李莎莎[1] 郑泉[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2016年第2期247-252,共6页Journal of Sichuan University(Natural Science Edition)

摘　　要：本文考虑Deligne-Simpson问题与Hurwitz计数问题的关系.本文首先观察到它们是不同群G上的相同代数方程(A_1,B_1)…(A_g,B_g)X_1…X_k=I的求解问题,然后计算了具有任意拆分的3阶Deligne-Simpson问题的欧拉特征类,并将其中一些特征类的生成函数表示成有理函数.In this paper,we consider the relationship between the Deligne-Simpson problem and Hurwitz enumeration problem.First,we observe that they are solutions of the same algebraic equation on different groups,which is（A1,B1）…（Ag,Bg）X1…Xk=I.Then we calculate Euler characteristic of the 3th order Deligne-Simpson problem with any partition,and express the generating function of some Euler characteristic as the rational functions.

关 键 词：Deligne-Simpson问题 Hurwitz计数问题 簇 欧拉特征类 

分 类 号：O187.2[理学—数学]