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TMF, 2009, Volume 161, Number 2, Pages 191–203 (Mi tmf6431)  

This article is cited in 17 scientific papers (total in 17 papers)

The $2{\times}2$ matrix Schlesinger system and the Belavin–Polyakov–Zamolodchikov system

D. P. Novikov

Omsk State Technical University, Omsk, Russia

Abstract: We show that the Belavin–Polyakov–Zamolodchikov equation of the minimal model of conformal field theory with the central charge $c=1$ for the Virasoro algebra is contained in a system of linear equations that generates the Schlesinger system with $2{\times}2$ matrices. This generalizes Suleimanov's result on the Painlevé equations. We consider the properties of the solutions, which are expressible in terms of the Riemann theta function.

Keywords: Belavin–Polyakov–Zamolodchikov equation, Schlesinger system, Painlevé equation, Garnier system

DOI: https://doi.org/10.4213/tmf6431

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English version:
Theoretical and Mathematical Physics, 2009, 161:2, 1485–1496

Bibliographic databases:

Received: 02.12.2008

Citation: D. P. Novikov, “The $2{\times}2$ matrix Schlesinger system and the Belavin–Polyakov–Zamolodchikov system”, TMF, 161:2 (2009), 191–203; Theoret. and Math. Phys., 161:2 (2009), 1485–1496

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. I. Suleimanov, ““Kvantovaya” linearizatsiya uravnenii Penleve kak komponenta ikh $L,A$ par”, Ufimsk. matem. zhurn., 4:2 (2012), 127–135  mathnet
    2. Gamayun O., Iorgov N., Lisovyy O., “Conformal Field Theory of Painlevé VI”, J. High Energy Phys., 2012, no. 10, 038  crossref  mathscinet  isi  elib  scopus
    3. Zabrodin A., Zotov A., “Quantum Painlevé-Calogero Correspondence”, J. Math. Phys., 53:7 (2012), 073507  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Novikov D.P., “A monodromy problem connected with $P_6$”, Painlevé equations and related topics, Degruyter Proceedings in Mathematics, Walter de Gruyter, Berlin, 2012, 123–128  mathscinet  isi
    5. H. Nagoya, Ya. Yamada, “Symmetries of quantum Lax equations for the Painlevé equations”, Ann. Henri Poincaré, 15:2 (2014), 313–344  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. B. I. Suleimanov, ““Quantizations” of Higher Hamiltonian Analogues of the Painlevé I and Painlevé II Equations with Two Degrees of Freedom”, Funct. Anal. Appl., 48:3 (2014), 198–207  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Conte R., Dornic I., “The Master Painlevé VI Heat Equation”, C. R. Math., 352:10 (2014), 803–806  crossref  mathscinet  zmath  isi  scopus
    8. Rosengren H., “Special Polynomials Related To the Supersymmetric Eight-Vertex Model: a Summary”, Commun. Math. Phys., 340:3 (2015), 1143–1170  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. Nagoya H., “Fractional Calculus of Quantum Painlevé Systems of Type _ ???”, Algebraic and Analytic Aspects of Integrable Systems and Painlev? Equations, Contemporary Mathematics, 651, eds. Dzhamay A., Maruno K., Ormerod C., Amer Mathematical Soc, 2015, 39–64  crossref  mathscinet  zmath  isi
    10. Rumanov I., “Beta Ensembles, Quantum Painlevé Equations and Isomonodromy Systems”, Algebraic and Analytic Aspects of Integrable Systems and Painlev? Equations, Contemporary Mathematics, 651, eds. Dzhamay A., Maruno K., Ormerod C., Amer Mathematical Soc, 2015, 125–155  crossref  mathscinet  zmath  isi
    11. D. P. Novikov, B. I. Suleimanov, ““Quantization” of an isomonodromic Hamiltonian Garnier system with two degrees of freedom”, Theoret. and Math. Phys., 187:1 (2016), 479–496  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. B. I. Suleimanov, “Quantum aspects of the integrability of the third Painlevé equation and a non-stationary time Schrödinger equation with the Morse potential”, Ufa Math. J., 8:3 (2016), 136–154  mathnet  crossref  mathscinet  isi  elib
    13. Gavrylenko P. Marshakov A., “Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations”, J. High Energy Phys., 2016, no. 2, 181  crossref  mathscinet  zmath  isi  elib  scopus
    14. V. A. Pavlenko, B. I. Suleimanov, ““Quantizations” of isomonodromic Hamilton system $H^{\frac{7}{2}+1}$”, Ufa Math. J., 9:4 (2017), 97–107  mathnet  crossref  isi  elib
    15. Conte R., “Generalized Bonnet Surfaces and Lax pairs of P-Vi”, J. Math. Phys., 58:10 (2017), 103508  crossref  mathscinet  zmath  isi  scopus
    16. Lencses M., Novaes F., “Classical Conformal Blocks and Accessory Parameters From Isomonodromic Deformations”, J. High Energy Phys., 2018, no. 4, 096  crossref  isi  scopus
    17. V. A. Pavlenko, B. I. Suleimanov, “Solutions to analogues of non-stationary Schrödinger equations defined by isomonodromic Hamilton system $H^{2+1+1+1}$”, Ufa Math. J., 10:4 (2018), 92–102  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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