Mamoru Ueda
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 $k+(m-n)(l-1)\neq0$.
Mamoru Ueda
This paper contains 7 sections, 18 theorems, 189 equations.
Theorem 1.1
Suppose that $m, n\geq2,m\neq n$ or $m\geq3,n=0$, and assume that $l\geq2$ and Then, there exists an algebra homomorphism where $\mathcal{U}(\mathcal{W}^{k}(\mathfrak{gl}(ml|nl),(l^{(m|n)})))$ is the universal enveloping algebra of $\mathcal{W}^{k}(\mathfrak{gl}(ml|nl),(l^{(m|n)}))$. Moreover, the image of $\Phi$ is dense in $\mathcal{U}(\mathcal{W}^{k}(\mathfrak{gl}(ml|nl),(l^{(m|n)})))$ provid
