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

2022/10/26 by Adachi, Shunya
#34M15 #34M35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.14729

Abstract

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 SU(p,q). When n≥ 3, the moduli space of irreducible monodromies can be realized as an affine algebraic set in ℂ^m for some m ∈ 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.

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