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arXiv · 2508.18769

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

Jyoichi Kaneko·Keiji Matsumoto·Katsuyoshi Ohara·Tomohide Terasoma
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Abstract

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 $B$.

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Jyoichi Kaneko, Keiji Matsumoto, Katsuyoshi Ohara, Tomohide Terasoma. 2025-08-26. The monodromy representation of a hypergeometric system in $m$ variables of rank $p^m$. https://arxiv.org/abs/2508.18769

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