Affine Super Yangians and Rectangular $W$-superalgebras

Abstract

In this paper, we construct a homomorphism from the affine super Yangian $Y_{\ve_1,\ve_2}(\widehat{\mathfrak{sl}}(m|n))$ to the universal enveloping algebra of the rectangular $W$-superalgebra $W^k(\mathfrak{gl}(ml|nl),(l^{(m|n)}))$. We also show that the image of this homomorphism is dense provided that $k+(m-n)(l-1)\ne 0$.

arXiv commentI added Section 6 in order to explain the relationships with the finite type

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• Quiver Yangian from Crystal Melting
• Rationality and Fusion Rules of Exceptional W-Algebras
• Screening operators and Parabolic inductions for Affine W-algebras (with an appendix by Shigenori Nakatsuka)
• A Note on Quiver Yangians and $\mathcal{R}$-Matrices
• Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras
• More on Affine Dynkin Quiver Yangians
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Affine Laumon spaces and iterated W-algebras
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• An Overview of Crystals and Double Quiver Yangians
• Twisted Affine Yangian and Rectangular $W$-algebra of type $D$
• Feigin-Semikhatov conjecture and related topics