Stokes phenomenon and reflection equations

TL;DR

This paper investigates the Stokes phenomenon in the cyclotomic Knizhnik-Zamolodchikov equation, establishing that its Stokes matrices satisfy key algebraic equations and exploring their connections to quantum algebraic structures.

Contribution

It demonstrates that the Stokes matrices of the cyclotomic KZ equation satisfy Yang-Baxter and reflection equations, linking Stokes phenomena with quantum symmetric pairs and associators.

Findings

Stokes matrices satisfy Yang-Baxter and reflection equations

Connections established between Stokes phenomena and quantum algebraic structures

Analysis of isomonodromy deformations in the cyclotomic KZ context

Abstract

In this paper, we study the Stokes phenomenon of the cyclotomic Knizhnik-Zamolodchikov equation, and prove that its two types of Stokes matrices satisfy the Yang-Baxter and reflection equations respectively. We then discuss its isomonodromy deformation, and its relations with cyclotomic associators, twists, and quantum symmetric pairs.