Abstract
The solvability of the Riemann-Hilbert problem for representations χ = χ 1 ⊕ χ 2 having the form of a direct sum is considered. It is proved that any representation χ 1 can be realized as a direct summand in the monodromy representation χ of a Fuchsian system. Other results are also obtained, which suggest a simple method for constructing counterexamples to the Riemann-Hilbert problem.
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