On the one-dimensional representations of finite $W$-superalgebras for $\mathfrak{gl}_{M|N}$

Fanlei Yang; Yang Zeng

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arXiv · 2409.16014

On the one-dimensional representations of finite $W$-superalgebras for $\mathfrak{gl}_{M|N}$

Fanlei Yang·Yang Zeng

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Abstract

Let $\mathfrak{g}=\mathfrak{gl}_{M|N}(\mathbb{k})$ be the general linear Lie superalgebra over an algebraically closed field $\mathbb{k}$ of characteristic zero. Fix an arbitrary even nilpotent element $e$ in $\mathfrak{g}$ and let $U(\mathfrak{g},e)$ be the finite $W$-superalgebra associated to the pair $(\mathfrak{g},e)$. In this paper we will give a complete classification of one-dimensional representations for $U(\mathfrak{g},e)$. To achieve this, we use the tool of shifted super Yangians to determine the commutative quotients of the finite $W$-superalgebras.

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BibTeX RIS

Fanlei Yang, Yang Zeng. 2024-09-24. On the one-dimensional representations of finite $W$-superalgebras for $\mathfrak{gl}_{M|N}$. https://arxiv.org/abs/2409.16014

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