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Unitary monodromies for rank two Fuchsian systems with $(n+1)$ singularities

Shunya Adachi
Oct 2022
摘要
We study the unitarity of monodromies for rank two Fuchsian systems of SLtype with $(n+1)$ regular singularities on the Riemann sphere, namely, we givea sufficient and necessary condition for the monodromy group to be conjugate toa subgroup of a special unitary group $\mathrm{SU}(p,q)$. When $n\ge 3$, themoduli space of irreducible monodromies can be realized as an affine algebraicset in $\mathbb{C}^m$ for some $m \in \mathbb{N}$. In this paper we give acharacterization and construction of unitary monodromies in terms of thisaffine algebraic set. The criterion of the signatures of unitary monodromies isalso given.
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