This article is cited in 3 papers

Irreducible Fuchsian system with reducible monodromy representation

I. V. Vyugin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We present an example of the reducible representation $\chi=\chi_1\oplus\chi_2$, which, on the one hand, is the monodromy representation of a Fuchsian system. On the other hand, the representation $\chi_2$ is a counterexample to the Riemann–Hilbert problem. Using a meromorphic gauge transformation, one cannot reduce this system to the direct sum of Fuchsian systems corresponding to the subrepresentations.

UDC: 517.927.7

Received: 02.06.2005

DOI: 10.4213/mzm2842

 English version: Mathematical Notes, 2006, 80:4, 478–484

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