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 $k+(m-n)(l-1)\ne 0$.

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

References in corpus (3)

• On Extensions of $\widehat{\mathfrak{gl}(m|n)}$ Kac-Moody algebras and Calabi-Yau Singularities
• Finite W-superalgebras via super Yangians
• The Surjectivity of the Evaluation Map of the Affine Super Yangian

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• More on Affine Dynkin Quiver Yangians
• Affine Laumon spaces and iterated W-algebras
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• An Overview of Crystals and Double Quiver Yangians
• Feigin-Semikhatov conjecture and related topics
• Twisted Affine Yangian and Rectangular $W$-algebra of type $D$