Twin-plane-partitions and N = 2 affine Yangian

Abstract

The universal enveloping algebra of W1+∞ is isomorphic to the affine Yangian of gl1. 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.