Critical points of master functions and the mKdV hierarchy of type A^2_2

TL;DR

This paper explores how the critical points of a specific master function related to the affine Lie algebra A^2_2 generate rational solutions to the mKdV hierarchy, linking algebraic structures to integrable systems.

Contribution

It introduces a novel connection between critical points of a master function for A^2_2 and rational solutions of the mKdV hierarchy.

Findings

Critical points generate rational solutions of the mKdV hierarchy.

The approach links affine Lie algebra structures to integrable systems.

Provides a new method to construct solutions using algebraic critical points.

Abstract

We consider the population of critical points generated from the critical point of the master function with no variables, which is associated with the trivial representation of the affine Lie algebra $A^2_2$. We describe how the critical points of this population define rational solutions of the equations of the mKdV hierarchy associated with $A^2_2$.