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

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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 161, Number 2, Pages 191–203
DOI: https://doi.org/10.4213/tmf6431 (Mi tmf6431)

This article is cited in 23 scientific papers (total in 23 papers)

The

2 \times 2

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

D. P. Novikov

Omsk State Technical University, Omsk, Russia

Full-text PDF (520 kB) Citations (23)

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

Abstract: We show that the Belavin–Polyakov–Zamolodchikov equation of the minimal model of conformal field theory with the central charge

c = 1

$c=1$ for the Virasoro algebra is contained in a system of linear equations that generates the Schlesinger system with

2 \times 2

$2{\times}2$ 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.

Received: 02.12.2008

English version:
Theoretical and Mathematical Physics, 2009, Volume 161, Issue 2, Pages 1485–1496
DOI: https://doi.org/10.1007/s11232-009-0135-y

Bibliographic databases:

Language: Russian

Citation: D. P. Novikov, “The

2 \times 2

$2{\times}2$ 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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Linking options:

https://www.mathnet.ru/eng/tmf6431

https://doi.org/10.4213/tmf6431

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This publication is cited in the following 23 articles:

V. A. Pavlenko, “Solutions of Analogs of Time-Dependent Schrödinger Equations Corresponding to a Pair of $H^{2+2+1}$ Hamiltonian Systems in the Hierarchy of Degenerations of an Isomonodromic Garnier System”, Diff Equat, 60:1 (2024), 77
Christian Hagendorf, Hjalmar Rosengren, “Nearest-Neighbour Correlation Functions for the Supersymmetric XYZ Spin Chain and Painlevé VI”, Commun. Math. Phys., 405:4 (2024)
V. A Pavlenko, “REShENIYa ANALOGOV VREMENNYKh URAVNENIY ShR¨EDINGERA, SOOTVETSTVUYuShchIKh PARE GAMIL'TONOVYKh SISTEM ????2+2+1 IERARKhII VYROZhDENIY IZOMONODROMNOY SISTEMY GARN'E”, Differencialʹnye uravneniâ, 60:1 (2024), 76
V. A. Pavlenko, “Solutions of the analogues of time-dependent Schrödinger equations corresponding to a pair of $H^{3+2}$ Hamiltonian systems”, Theoret. and Math. Phys., 212:3 (2022), 1181–1192
B. I. Suleimanov, “Isomonodromic quantization of the second Painlevé equation by means of conservative Hamiltonian systems with two degrees of freedom”, St. Petersburg Math. J., 33:6 (2022), 995–1009
Lencses M., Novaes F., “Classical Conformal Blocks and Accessory Parameters From Isomonodromic Deformations”, J. High Energy Phys., 2018, no. 4, 096
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
V. A. Pavlenko, B. I. Suleimanov, ““Quantizations” of isomonodromic Hamilton system $H^{\frac{7}{2}+1}$ ”, Ufa Math. J., 9:4 (2017), 97–107
Conte R., “Generalized Bonnet Surfaces and Lax pairs of P-Vi”, J. Math. Phys., 58:10 (2017), 103508
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
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
Gavrylenko P. Marshakov A., “Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations”, J. High Energy Phys., 2016, no. 2, 181
Rosengren H., “Special Polynomials Related To the Supersymmetric Eight-Vertex Model: a Summary”, Commun. Math. Phys., 340:3 (2015), 1143–1170
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
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
A. Zabrodin, A. Zotov, “Classical-quantum correspondence and functional relations for Painlevé equations”, Constr. Approx., 41:3 (2015), 385–423
H. Nagoya, Ya. Yamada, “Symmetries of quantum Lax equations for the Painlevé equations”, Ann. Henri Poincaré, 15:2 (2014), 313–344
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
Conte R., Dornic I., “The Master Painlevé VI Heat Equation”, C. R. Math., 352:10 (2014), 803–806
B. I. Suleimanov, ““Kvantovaya” linearizatsiya uravnenii Penleve kak komponenta ikh $L,A$ par”, Ufimsk. matem. zhurn., 4:2 (2012), 127–135

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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