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

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.

arXiv comment67 pages; v3: minor corrections

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• Super-Schur Polynomials for Affine Super Yangian $\mathsf{Y}({\widehat{\mathfrak{gl}}}_{1|1})$
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• Towards the theory of Yangians
• An Overview of Crystals and Double Quiver Yangians