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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 Painleve 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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Submitted on : Tuesday, July 10, 2018 - 1:08:00 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM

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Pavlo Gavrylenko, Nikolai Iorgov, Oleg Lisovyy. On solutions of the Fuji-Suzuki-Tsuda system. SIGMA, 2018, 14, pp.123. ⟨10.3842/SIGMA.2018.123⟩. ⟨hal-01833765⟩

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