The refined solution to the Capelli eigenvalue problem for $\mathfrak{gl}(m|n)\oplus \mathfrak{gl}(m|n)$ and $\mathfrak{gl}(m|2n)$

Mengyuan Cao, Monica Nevins, Hadi Salmasian

Let $\mathfrak{g}$ be either the Lie superalgebra $\mathfrak{gl}(V)\oplus \mathfrak{gl}(V)$ where $V:={\mathbb{C}}^{m|n}$ or the Lie superalgebra $\mathfrak{gl}(V)$ where $V:=\mathbb C^…