高阶Fuchsian ODE的微分Galois群
Differential Galois groups of high order Fuchsian ODE's
摘要：
我们提出了一个简单的，但有效的，方法来计算连接矩阵之间的独立的本地解决方案，定义在两个相邻的奇点，Fuchsian微分方程的相当大的订单，如发现的第三和第四贡献（$χ^{(3)}$和$χ^{(4)}$）的磁化率的正方形晶格伊辛模型。我们使用前面的连接矩阵得到的所有单值矩阵的Fuchsian微分方程的$χ^{(3)}$（和$χ^{(4)}$）表示在相同的基础上的解决方案。这些单值矩阵是$χ^{(3)}$（和$χ^{(4)}$）的Fuchsian微分方程的微分伽罗瓦群的生成元，其分析在这里刚刚画出。
英文摘要：
We present a simple, but efficient, way to calculate connection matrices between sets of independent local solutions, defined at two neighboring singular points, of Fuchsian differential equations of quite large orders, such as those found for the third and fourth contribution ($χ^{(3)}$ and $χ^{(4)}$) to the magnetic susceptibility of square lattice Ising model. We use the previous connection matrices to get the exact explicit expressions of all the monodromy matrices of the Fuchsian differential equation for $χ^{(3)}$ (and $χ^{(4)}$) expressed in the same basis of solutions. These monodromy matrices are the generators of the differential Galois group of the Fuchsian differential equations for $χ^{(3)}$ (and $χ^{(4)}$), whose analysis is just sketched here.
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