Stokes Phenomenon and Yangians

TL;DR

This paper explores the relationship between Yangians and Stokes phenomena in hypergeometric differential equations, revealing how Stokes matrices can be expressed through Yangian representations and analyzing their algebraic structures.

Contribution

It establishes a novel connection between Yangians and the Stokes matrices of hypergeometric equations, using difference systems and algebroid structures.

Findings

Stokes matrices expressed as infinite products of Yangian representations

Connection between Yangians and solutions of quantum hypergeometric equations

Analysis of the algebroid structure associated with Stokes matrices

Abstract

In this paper, we first establish a connection between Yangians and the unique formal solution of the quantum hypergeometric differential equations at irregular singularities. We then realize the Stokes matrices of the hypergeometric equations as infinite matrix products of representations of Yangains, with the help of the theory of difference systems. Along the way, we also investigate the algebroid structure associated with the Stokes matrices.