Geodesic
Fuchsian Systems with Reducible Monodromy Are Meromorphically
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 481-490

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In this paper it is shown that each Fuchsian system whose representation of monodromy is reducible can be transformed, by means of a meromorphic gauge transformation, into a Fuchsian system with reducible set of coefficients. 
@article{TM_2002_236_a47,
     author = {S. Malek},
     title = {Fuchsian {Systems} with {Reducible} {Monodromy} {Are} {Meromorphically}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {481--490},
     publisher = {mathdoc},
     volume = {236},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a47/}
}
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S. Malek. Fuchsian Systems with Reducible Monodromy Are Meromorphically. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 481-490. http://geodesic.mathdoc.fr/item/TM_2002_236_a47/