标题： 超几何系统在$m$变量中的单值表示，其秩为$p^m$ 显示英文标题

标题： The monodromy representation of a hypergeometric system in $m$ variables of rank $p^m$

摘要： 我们研究超几何系统$\mathcal{F}_{C}^{p,m}(a,B)$在$m$个变量中，秩为$p^m$，参数为$a$和$B$的单值表示。 该系统可以看作是秩为$p$的广义超几何方程的多变量模型。 We construct $m+1$ loops which generate the fundamental group of the complement of the singular locus of $\mathcal{F}_{C}^{p,m}(a,B)$, and we show that they satisfy certain relations as elements of the fundamental group. We produce circuit matrices along these loops with respect to a fundamental system of solutions to $\mathcal{F}_C^{p,m}(a,B)$ under certain non-integrality conditions on parameters $a$ and $B$. 显示英文摘要

摘要： We study the monodromy representation of the hypergeometric system $\mathcal{F}_{C}^{p,m}(a,B)$ in $m$ variables of rank $p^m$ with parameters $a$ and $B$. This system can be regarded as a multi-variable model of the generalized hypergeometric equation of rank $p$. We construct $m+1$ loops which generate the fundamental group of the complement of the singular locus of $\mathcal{F}_{C}^{p,m}(a,B)$, and we show that they satisfy certain relations as elements of the fundamental group. We produce circuit matrices along these loops with respect to a fundamental system of solutions to $\mathcal{F}_C^{p,m}(a,B)$ under certain non-integrality conditions on parameters $a$ and $B$.