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On Solutions of the Fuji-Suzuki-Tsuda System
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2018. Vol. 14. P. 1-27.
Gavrylenko P., Iorgov N., Lisovyy O.
We derive Fredholm determinant and series representation of the tau function of the Fuji-Suzuki-Tsuda system and its multivariate extension, thereby generalizing to higher rank the results obtained for Painlevé VI and the Garnier system. A special case of our construction gives a higher rank analog of the continuous hypergeometric kernel of Borodin and Olshanski. We also initiate the study of algebraic braid group dynamics of semi-degenerate monodromy, and obtain as a byproduct a direct isomonodromic proof of the AGT-W relation for $c=N-1$.
Keywords: изомонодромные деформацииisomonodromic deformationsFredholm determinantдетерминант Фредгольма
Publication based on the results of:
Gavrylenko P., Lisovyy O., / Cornell University. Series math-ph "arXiv". 2016. No. 1608.00958.
We derive Fredholm determinant representation for isomonodromic tau functions of Fuchsian systems with n regular singular points on the Riemann sphere and generic monodromy in GL(N,ℂ). The corresponding operator acts in the direct sum of N(n−3) copies of L2(S1). Its kernel has a block integrable form and is expressed in terms of fundamental solutions of ...
Added: September 20, 2016
Gavrylenko P., Lisovyy O., / arXiv.org. Series arXiv.org "math-ph". 2017. No. 1705.01869.
We show that the dual partition function of the pure $\mathcal N=2$ $SU(2)$ gauge theory in the self-dual $\Omega$-background (a) is given by Fredholm determinant of a generalized Bessel kernel and (b) coincides with the tau function associated to the general solution of the Painlev\'e III equation of type $D_8$ (radial sine-Gordon equation). In particular, ...
Added: May 5, 2017
Cafasso M., Gavrylenko P., Lisovyy O., Communications in Mathematical Physics 2019 Vol. 365 No. 2 P. 741-772
We define a tau function for a generic Riemann–Hilbert problem posed on a union of non-intersecting smooth closed curves with jump matrices analytic in their neighborhood. The tau function depends on parameters of the jumps and is expressed as the Fredholm determinant of an integral operator with block integrable kernel constructed in terms of elementary ...
Added: September 12, 2018
Gavrylenko P., Marshakov A., / Cornell University. Series "Working papers by Cornell University". 2015. No. 1507.08794.
We consider the conformal blocks in the theories with extended conformal W-symmetry for the integer Virasoro central charges. We show that these blocks for the generalized twist fields on sphere can be computed exactly in terms of the free field theory on the covering Riemann surface, even for a non-abelian monodromy group. The generalized twist ...
Added: October 14, 2015
Gavrylenko P., Lisovyy O., Communications in Mathematical Physics 2018 Vol. 363 No. 1 P. 1-58
We derive Fredholm determinant representation for isomonodromic tau functions of Fuchsian systems with n regular singular points on the Riemann sphere and generic monodromy in GL (N,ℂ). The corresponding operator acts in the direct sum of N (n − 3) copies of L2 (S1). Its kernel has a block integrable form and is expressed in ...
Added: September 12, 2018
Poberezhny V. A., / ИТЭФ. Series "Препринты ИТЭФ". 2014. No. 50.14.
We prove that any non-resonant Fuchsian system with commutative monodromy is in fact a commutative system, that is a system with commuting residues. For logarithmic connection that Fuchsian system presents that implies the triviality of its isomonodromic deformations. ...
Added: March 26, 2015
Poberezhny V. A., / ИТЭФ. Series "Препринты ИТЭФ". 2012. No. 57/12.
In this work we investigate the action of generalized Schlesinger transformation on the isomonodromic families of meromorphic connections on the linear bundles of rank two and degree zero over an elliptic curve. The main interest is the action of the gauge transformation on the moduli space of vector bundles. the central result is the explicit ...
Added: March 31, 2014
Glutsyuk A., Bibilo Y., / Cornell University. Series arXiv "math". 2021. No. 2011.07839.
We study family of dynamical systems on 2-torus modeling over-damped Josephson junction in superconductivity. It depends on three parameters (B,A;ω): B (abscissa), A(ordinate), ω (a fixed frequency).We study the rotation numberρ(B,A;ω) as a function of (B,A) withfixedω. Aphase-lock areais the level set Lr:={ρ=r}, if it has an on-empty interior. This holds for r∈Z (a result ...
Added: November 26, 2020
Zabrodin A., Zotov A., Journal of Mathematical Physics 2012 Vol. 53 No. 7 P. 073508-1-073508-19
This paper is a continuation of our previous paper where the Painlevé-Calogero correspondence has been extended to auxiliary linear problems associated with Painlevé equations. We have proved, for the first five equations from the Painlevé list, that one of the linear problems can be recast in the form of the non-stationary Schrödinger equation whose Hamiltonian ...
Added: September 19, 2012
Gavrylenko P., Iorgov N., Lisovyy O., Letters in Mathematical Physics 2020 Vol. 110 No. 2 P. 327-364
We construct the general solution of a class of Fuchsian systems of rank N as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of WN-algebra with central charge c = N − 1. The simplest example is given by the tau function of the FujiSuzuki-Tsuda system, expressed as a Fourier ...
Added: August 20, 2020
V. A. Poberezhny, Journal of Mathematical Sciences 2013 Vol. 195 No. 4 P. 533-540
We consider systems of linear differential equations discussing some classical and modern results in the Riemann problem, isomonodromic deformations, and other related topics. Against this background, we illustrate the relations between such phenomena as the integrability, the isomonodromy, and the Painlevé property. The recent advances in the theory of isomonodromic deformations presented show perfect agreement ...
Added: February 14, 2014
Levin A., Ольшанецкий М. А., Зотов А. В., Успехи математических наук 2014 Т. 69 № 1(415) С. 39-124
В данной работе изомонодромные задачи описываются в терминах плоских G-расслоений на проколотых эллиптических кривых Σ_τ и связностей с регулярными особенностями в отмеченных точках. Расслоения классифицируются по их характеристическим классам, которые являются элементами группы вторых когомологий H^2(Σ_τ,Z(G)), где Z(G) – центр G. По каждой простой комплексной группе Ли G и произвольному характеристическому классу определяется пространство модулей ...
Added: January 21, 2015
Gavrylenko P., Journal of High Energy Physics 2015 No. 09 P. 167
We study the solution of the Schlesinger system for the 4-point $\mathfrak{sl}_N$ isomonodromy problem and conjecture an expression for the isomonodromic τ-function in terms of 2d conformal field theory beyond the known N = 2 Painlevé VI case. We show that this relation can be used as an alternative definition of conformal blocks for the ...
Added: October 9, 2015
Gontsov R. R., V.A. Poberezhnyi, Helminck G. F., Russian Mathematical Surveys 2011 Vol. 66 No. 1 P. 63-105
This article concerns deformations of meromorphic linear differential systems. Problems relating to their existence and classification are reviewed, and the global and local behaviour of solutions to deformation equations in a neighbourhood of their singular set is analysed. Certain classical results established for isomonodromic deformations of Fuchsian systems are generalized to the case of integrable ...
Added: September 27, 2013
Vladimir Poberezhny, Acta Applicandae Mathematicae: An International Survey Journal on Applying Mathematics and Mathematical Applications 2008 Vol. 101 No. 1-3 P. 255-263
We give a review of the modern theory of isomonodromic deformations of Fuchsian systems discussing both classical and modern results, such as a general form of the isomonodromic deformations of Fuchsian systems, their differences from the classical Schlesinger deformations, the Fuchsian system moduli space structure and the geometric meaning of new degrees of freedom appeared ...
Added: September 28, 2013
Bershtein M., Gavrylenko P., Marshakov A., Journal of High Energy Physics 2018 Vol. 08 No. 108 P. 1-54
We study the twist-field representations of W-algebras and generalize construction of the corresponding vertex operators to D- and B-series. It is shown, how the computation of characters of these representations leads to nontrivial identities involving lattice theta-functions. We also propose a way to calculate their exact conformal blocks, expressing them for D-series in terms of ...
Added: September 11, 2018
Zabrodin A., Zotov A., Journal of Mathematical Physics 2012 Vol. 53 No. 7 P. 073507-1-073507-19
The Painlevé-Calogero correspondence is extended to auxiliary linear problems associated with Painlevé equations. The linear problems are represented in a new form which has a suggestive interpretation as a "quantized" version of the Painlevé-Calogero correspondence. Namely, the linear problem responsible for the time evolution is brought into the form of non-stationary Schrödinger equation in imaginary ...
Added: September 19, 2012
De Gruyter Mouton, 2012
A local behaviour of solutions of Schlesinger equation ia studied. We obtain expansions for this solutions, which converge in some neighborhood of singular point. As a corollary the similar result for the sixth Painleve equation was obtained. In our analysis, we use the isomonodromic approach to solve this problem. ...
Added: February 19, 2013
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017