# 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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Article dans une revue
SIGMA, 2018, 14, pp.123. 〈10.3842/SIGMA.2018.123〉

https://hal.archives-ouvertes.fr/hal-01833765
Contributeur : Inspire Hep <>
Soumis le : mardi 10 juillet 2018 - 01:08:00
Dernière modification le : mercredi 13 mars 2019 - 17:14:30

### Citation

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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