Finite W-superalgebras via super Yangians

Abstract: Let $e$ be an arbitrary even nilpotent element in the general linear Lie superalgebra $\mathfrak{gl}{M|N}$ and let $\mathcal{W}_e$ be the associated finite $W$-superalgebra. Let $Y{m|n}$ be the super Yangian associated to the Lie superalgebra $\mathfrak{gl}{m|n}$. A subalgebra of $Y{m|n}$, called the shifted super Yangian and denoted by $Y_{m|n}(\sigma)$, is defined and studied. Moreover, an explicit isomorphism between $\mathcal{W}e$ and a quotient of $Y{m|n}(\sigma)$ is established.