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Matematicheskie Zametki, 2009, Volume 85, Issue 6, Pages 817–825
DOI: https://doi.org/10.4213/mzm7660 (Mi mzm7660) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Fuchsian Systems with Completely Reducible Monodromy

I. V. Vyugin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (423 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm7660
Abstract: The solvability of the Riemann–Hilbert problem for representations χ=χ1⊕χ2 having the form of a direct sum is considered. It is proved that any representation χ1 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.
Keywords: Riemann–Hilbert problem, decomposable Fuchsian system, completely reducible monodromy, (semi)stable bundle with connection, holomorphic (meromorphic) function.
Received: 20.06.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 6, Pages 780–786
DOI: https://doi.org/10.1134/S0001434609050204
Bibliographic databases:
UDC: 517
Language: Russian
Citation: I. V. Vyugin, “Fuchsian Systems with Completely Reducible Monodromy”, Mat. Zametki, 85:6 (2009), 817–825; Math. Notes, 85:6 (2009), 780–786
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    1. I. V. Vyugin, L. A. Dudnikova, “Stable vector bundles and the Riemann–Hilbert problem on a Riemann surface”, Sb. Math., 215:2 (2024), 141–156  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. D. V. Anosov, V. P. Leksin, “Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations”, Russian Math. Surveys, 66:1 (2011), 1–33  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. R. R. Gontsov, V. A. Poberezhnyi, G. F. Helminck, “On deformations of linear differential systems”, Russian Math. Surveys, 66:1 (2011), 63–105  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. I. V. Vyugin, “Riemann–Hilbert problem for scalar Fuchsian equations and related problems”, Russian Math. Surveys, 66:1 (2011), 35–62  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    Citing articles in Google Scholar: Russian citations, English citations
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