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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 123, 27 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.123 (Mi sigma1422) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On Solutions of the Fuji–Suzuki–Tsuda System

Pavlo Gavrilenkoabc, Nikolai Iorgovcd, Oleg Lisovyye

a Center for Advanced Studies, Skolkovo Institute of Science and Technology, 143026 Moscow, Russia
b National Research University Higher School of Economics, International Laboratory of Representation Theory and Mathematical Physics, Moscow, Russia
c Bogolyubov Institute for Theoretical Physics, 03143 Kyiv, Ukraine
d Kyiv Academic University, 36 Vernadsky Ave., 03142 Kyiv, Ukraine
e Institut Denis-Poisson, Université de Tours, Parc de Grandmont, 37200 Tours, France
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DOI: https://doi.org/10.3842/SIGMA.2018.123
Abstract: 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: isomonodromic deformations; Painlevé equations; Fredholm determinants.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
Russian Science Foundation 16-11-10160
National Academy of Sciences of Ukraine 0117U000238
0117U000240
The work of P.G. was partially supported by the Russian Academic Excellence Project ‘5-100’ and by the RSF grant No. 16-11-10160. In particular, the results of Section 6 were obtained using support of Russian Science Foundation. P.G. is a Young Russian Mathematics award winner and would like to thank its sponsors and jury. N.I. was partially supported by the National Academy of Sciences of Ukraine (project No. 0117U000238), by the Program of Fundamental Research of the Department of Physics and Astronomy of the NAS of Ukraine (project No. 0117U000240), and by the ICTP-SEENET-MTP project NT-03: Cosmology – Classical and Quantum Challenges.
Received: June 22, 2018; in final form October 30, 2018; Published online November 11, 2018
Bibliographic databases:
Document Type: Article
MSC: 33E17; 34M55; 34M56
Language: English
Citation: Pavlo Gavrilenko, Nikolai Iorgov, Oleg Lisovyy, “On Solutions of the Fuji–Suzuki–Tsuda System”, SIGMA, 14 (2018), 123, 27 pp.
Citation in format AMSBIB
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\paper On Solutions of the Fuji--Suzuki--Tsuda System
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\totalpages 27
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