Abstract
The affine Yangian of \( {\mathfrak{gl}}_1 \) is isomorphic to the universal enveloping algebra of \( {\mathcal{W}}_{1+\infty } \) and can serve as a building block in the construction of new vertex operator algebras. In [1], a two-parameter family generalization of \( \mathcal{N} \) = 2 supersymmetric \( {\mathcal{W}}_{\infty } \) algebra was constructed by “gluing” two affine Yangians of \( {\mathfrak{gl}}_1 \) using operators that transform as (□, \( \overline{\square} \)) and (\( \overline{\square} \), □) w.r.t. the two affine Yangians. In this paper we realize a similar (but non-isomorphic) two-parameter gluing construction where the gluing operators transform as (□, □) and (\( \overline{\square} \), \( \overline{\square} \)) w.r.t. the two affine Yangians. The corresponding representation space consists of pairs of plane partitions connected by a common leg whose cross-section takes the shape of Young diagrams, offering a more transparent geometric picture than the previous construction.
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Li, W. Gluing affine Yangians with bi-fundamentals. J. High Energ. Phys. 2020, 182 (2020). https://doi.org/10.1007/JHEP06(2020)182
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DOI: https://doi.org/10.1007/JHEP06(2020)182