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

Fanlei Yang, Yang Zeng

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 e…