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 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 $c=N-1$.

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

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Cited by in corpus (5)

• A slow review of the AGT correspondence
• 2-parameter $\tau$-function for the first Painlevé equation -Topological recursion and direct monodromy problem via exact WKB analysis-
• Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions
• Painlevé/CFT correspondence on a torus
• On $q$-Isomonodromic Deformations and $q$-Nekrasov Functions