Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds

Jiakang Bao

doi:10.1088/1751-8121/acd037

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arXiv · 2208.13395

Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds

Jiakang Bao

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Abstract

We focus on quiver Yangians for most generalized conifolds. We construct a coproduct of the quiver Yangian following the similar approach by Guay-Nakajima-Wendlandt. We also prove that the quiver Yangians related by Seiberg duality are indeed isomorphic. Then we discuss their connections to $\mathcal{W}$-algebras analogous to the study by Ueda. In particular, the universal enveloping algebras of the $\mathcal{W}$-algebras are truncations of the quiver Yangians, and therefore they naturally have truncated crystals as their representations.

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Jiakang Bao. 2022-08-29. Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds. https://doi.org/10.1088/1751-8121%2Facd037

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