Braid Group Action on Affine Yangian

TL;DR

This paper investigates how braid groups act on Yangians related to Kac-Moody Lie algebras, specifically demonstrating that the affine Yangian of type A's evaluation map encompasses the diagonal Heisenberg algebra.

Contribution

It introduces a braid group action on affine Yangians and proves the image of the evaluation map contains the diagonal Heisenberg algebra.

Findings

Braid group actions on Yangians are constructed.

The evaluation map's image includes the diagonal Heisenberg algebra.

Application to affine Yangian of type A demonstrates the algebraic structure containment.

Abstract

We study braid group actions on Yangians associated with symmetrizable Kac-Moody Lie algebras. As an application, we focus on the affine Yangian of type A and use the action to prove that the image of the evaluation map contains the diagonal Heisenberg algebra inside $\hat{\mathfrak{gl}}_N$.