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 Gamier 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.
On Solutions of the Fuji-Suzuki-Tsuda System / Gavrylenko, P; Iorgov, N; Lisovyy, O. - In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. - ISSN 1815-0659. - 14:(2018), pp. 1-27. [10.3842/SIGMA.2018.123]
On Solutions of the Fuji-Suzuki-Tsuda System
Gavrylenko, P;
2018-01-01
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 Gamier 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.| File | Dimensione | Formato | |
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