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 $k+(m-n)(l-1)\neq0$.