4 problems

Let $\mathfrak{g}$ be the Lie superalgebra and $e$ the nilpotent element defining the finite $W$-superalgebra $U(\mathfrak{g},e)$. Let $Z(U(\mathfrak{g}))$ and…

Let $\mathfrak{g}$ be a basic Lie superalgebra over $\mathbb{C}$, let $e\in\mathfrak{g}_{\bar 0}$ be nilpotent, and let $\chi$ be the corresponding linear function on…

Let $\mathfrak{g}=\mathfrak{g}_{\bar 0}+\mathfrak{g}_{\bar 1}$ be a basic Lie superalgebra over $\mathbb{C}$, let $e\in\mathfrak{g}_{\bar 0}$ be nilpotent, and let $\mathsf{r}$ be…

Let $\mathfrak{g}$ be a basic Lie superalgebra over $\mathbb{C}$, let $e\in\mathfrak{g}_{\bar 0}$ be nilpotent, and set $d_1=\dim\mathfrak{g}_{\bar 1}-\dim\mathfrak{g}^e_{\bar 1}$.…