Anton Alekseev

collaborators

4 papers

math.QA2026

The kernel of formal polylogarithms

Anton Alekseev, Megan Howarth, Florian Naef +2

Polylogarithmic functions (polylogs) in $n$ variables can be viewed as elements of $(U p_{m})^{*}$ , the dual of the universal enveloping algebra of the Lie algebra $\mathfr…

math.QA2024

Poisson brackets and coaction maps of regularized holonomies of the KZ equation

Anton Alekseev, Florian Naef, Muze Ren

We derive explicit closed formulas for the Kirillov-Kostant-Souriau (KKS) coaction maps of open path regularized holonomies of the Knizhnik-Zamolodchikov (KZ) equation, and the cor…

math-ph2024

WKB asymptotics of Stokes matrices, spectral curves and rhombus inequalities

Anton Alekseev, Andrew Neitzke, Xiaomeng Xu +1

We consider an $n \times n$ system of ODEs on $P^{1}$ with a simple pole $A$ at $z = 0$ and a double pole $u = diag (u_{1}, \dots, u_{n})$ at $z = \infty$ . This is the simplest si…

math.QA2024

Generalized Pentagon Equations

Anton Alekseev, Florian Naef, Muze Ren

Drinfeld defined the Knizhinik--Zamolodchikov (KZ) associator $Φ_{KZ}$ by considering the regularized holonomy of the KZ connection along the {\em droit chemin} $[0, 1]$ . The KZ…