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arXiv · 2001.08718

Finite W-superalgebras via super Yangians

Yung-Ning Peng
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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.

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BibTeXRIS

Yung-Ning Peng. 2020-01-23. Finite W-superalgebras via super Yangians. https://doi.org/10.1016/j.aim.2020.107459

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