Braid Group Action on Affine Yangian

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 ${\widehat{\mathfrak{g}\mathfrak{l}}}_N$.