Monday, 30 July, 2018

## Published in:

arXiv:1807.11304

The universal enveloping algebra of {\cal W}_{1+\infty} is isomorphic to the affine Yangian of \mathfrak{gl}_1. We study the N=2 supersymmetric version of this correspondence, and identify the full set of defining relations of the supersymmetric affine Yangian. These relations can be deduced by demanding that the algebra has a representation on twin-plane-partitions, which we construct by gluing pairs of plane partitions. We define the action of the algebra on these twin-plane-partitions explicitly.