具有$(n+1)$个奇点的二阶Fuchsian系统的酉单值群
Unitary monodromies of rank two Fuchsian systems with $(n+1)$ singularities
AI总结：
本文研究带$(n+1)$个正则奇点的SL型二阶Fuchsian系统单值群的酉性，给出其共轭于$\mathrm{SU}(p,q)$子群的充要条件，利用仿射代数集刻画构造酉单值群并分类其符号差。
摘要：
我们研究了黎曼球面上具有$(n+1)$个正则奇点的SL型二阶Fuchsian系统的单值群的酉性，即给出了单值群共轭于特殊酉群$\mathrm{SU}(p,q)$的子群的充要条件。当$n\ge 3$时，不可约单值群的模空间可实现为$\mathbb{C}^m$中的仿射代数集，其中$m \in \mathbb{N}$。本文利用该仿射代数集给出了酉单值群的刻画与构造，还对酉单值群的符号差进行了分类。
英文摘要：
We study the unitarity of monodromies of rank two Fuchsian systems of SL type with $(n+1)$ regular singularities on the Riemann sphere, namely, we give a sufficient and necessary condition for the monodromy group to be conjugate to a subgroup of a special unitary group $\mathrm{SU}(p,q)$. When $n\ge 3$, the moduli space of irreducible monodromies can be realized as an affine algebraic set in $\mathbb{C}^m$ for some $m \in \mathbb{N}$. In this paper, we give a characterization and construction of unitary monodromies in terms of this affine algebraic set. The signatures of unitary monodromies are also classified.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
