On Solutions of the Fuji-Suzuki-Tsuda System

Abstract

We derive the 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 the algebraic braid group dynamics of semi-degenerate monodromy and, as a byproduct, obtain a direct isomonodromic proof of the AGT-W relation for c = N−1.