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Finite W-superalgebras via super Yangians (2001.08718v2)
Published 23 Jan 2020 in math.QA and math.RT
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.