On solutions of the Fuji-Suzuki-Tsuda system

Pavlo Gavrylenko; Nikolai Iorgov; Oleg Lisovyy

doi:10.3842/SIGMA.2018.123

On solutions of the Fuji-Suzuki-Tsuda system

Pavlo Gavrylenko
, Nikolai Iorgov
, Oleg Lisovyy

Mathematics

Research output: Contribution to journal › Article › peer-review

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 $c=N-1$.

Original language	English
Journal	SIGMA
DOIs	https://doi.org/10.3842/SIGMA.2018.123
Publication status	Published - 22 Jun 2018

Bibliographical note

A contribution to the Special Issue on Painlevé Equations and Applications in Memory of Andrei Kapaev

Keywords

math-ph

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10.3842/SIGMA.2018.123

1806.08650v2

Cite this

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title = "On solutions of the Fuji-Suzuki-Tsuda system",

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 Painlev{\'e} 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\$.",

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T1 - On solutions of the Fuji-Suzuki-Tsuda system

AU - Gavrylenko, Pavlo

AU - Iorgov, Nikolai

AU - Lisovyy, Oleg

N1 - A contribution to the Special Issue on Painlevé Equations and Applications in Memory of Andrei Kapaev

PY - 2018/6/22

Y1 - 2018/6/22

N2 - 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 $c=N-1$.

AB - 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 $c=N-1$.

KW - math-ph

U2 - 10.3842/SIGMA.2018.123

DO - 10.3842/SIGMA.2018.123

M3 - Article

JO - SIGMA

JF - SIGMA

ER -

On solutions of the Fuji-Suzuki-Tsuda system

Abstract

Bibliographical note

Keywords

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