Highest weight theory for minimal finite $W$-superalgebras and related Whittaker categories

Yang Zeng, Bin Shu

Let $\mathfrak{g}={\mathfrak{g}}_{\bar{0}}+{\mathfrak{g}}_{\bar{1}}$ be a basic classical Lie superalgebra over $\mathbb{C}$, and $e=e_{\theta }\in {\mathfrak{g}}_{\bar{0}}$ with $-\theta$ being a minimal r…