Asymptotic analysis of the confluent Dotsenko-Fateev system

Abstract

The Dotsenko-Fateev equation is a third-order linear ordinary differential equation studied in two-dimensional conformal field theory. We study the confluent Dotsenko-Fateev system, a rank-three system of linear ordinary differential equations obtained by confluence from a first-order system equivalent to the Dotsenko-Fateev equation. It has an irregular singular point at infinity, and its solutions admit double integral representations of confluent Selberg type. Using these representations, we construct sectorial fundamental solution matrices around infinity, establish their asymptotic expansions, and determine the associated Stokes matrices explicitly. We further study three aspects of the confluent Dotsenko-Fateev system: its equivalence to the degree-two polynomial reduction of the Schrödinger equation for the quantum Painlevé equation of type V, its realization as a restriction of a confluent version of the linear Pfaffian system associated with Appell's hypergeometric function $F_4$, and its reduction to the trivial rank-one equation via integral transforms and a quadratic change of the independent variable.