English

On solutions of the Fuji-Suzuki-Tsuda system

Mathematical Physics 2018-11-13 v2 math.MP

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 Painlev\'e 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=N1c=N-1.

Keywords

Cite

@article{arxiv.1806.08650,
  title  = {On solutions of the Fuji-Suzuki-Tsuda system},
  author = {Pavlo Gavrylenko and Nikolai Iorgov and Oleg Lisovyy},
  journal= {arXiv preprint arXiv:1806.08650},
  year   = {2018}
}

Comments

A contribution to the Special Issue on Painlev\'e Equations and Applications in Memory of Andrei Kapaev