### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 020, 28 pages      arXiv:1805.01621      https://doi.org/10.3842/SIGMA.2019.020

### Braid Group Action on Affine Yangian

Ryosuke Kodera
Department of Mathematics, Graduate School of Science, Kobe University, Kobe 657-8501, Japan

Received August 09, 2018, in final form February 27, 2019; Published online March 16, 2019

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 $\hat{\mathfrak{gl}}_N$.

Key words: affine Yangian; braid group action; evaluation map.

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