Abstract
The universal enveloping algebra of \( \mathcal{W} \)1+∞ is isomorphic to the affine Yangian of \( \mathfrak{g}{\mathfrak{l}}_1 \). We study the \( \mathcal{N} \) = 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.
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Gaberdiel, M.R., Li, W. & Peng, C. Twin-plane-partitions and \( \mathcal{N} \) = 2 affine Yangian. J. High Energ. Phys. 2018, 192 (2018). https://doi.org/10.1007/JHEP11(2018)192
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DOI: https://doi.org/10.1007/JHEP11(2018)192