Twin-plane-partitions and $\mathcal{N}=2$ affine Yangian

Abstract

The universal enveloping algebra of ${\mathcal{W}}_{1+\infty }$ is isomorphic to the affine Yangian of ${\mathfrak{gl}}_1$. 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.

arXiv comment61 pages, 14 figures, 2 tables

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• Gluing two affine Yangians of ${\mathfrak{gl}}_1$
• Chiral Algebras of Two-Dimensional SYK Models
• Plane Partition Realization of (Web of) W-algebra Minimal Models
• A Note on Quiver Yangians and $\mathcal{R}$-Matrices
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• Crystal Melting, BPS Quivers and Plethystics
• Gauge origami and quiver W-algebras IV: Pandharipande--Thomas $qq$-characters
• The Grassmannian VOA
• The matrix-extended $W_{1+\infty }$ algebra
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