In this paper, we extend the results of Grantcharov and Robitaille in 2021 on mixed tensor products and Capelli determinants to the superalgebra setting. Specifically, we construct a family of superalgebra homomorphisms \(\varphi _R: U(\mathfrak {gl}(m+1|n)) \rightarrow \mathcal {D}'(m|n) \otimes U(\mathfrak {gl}(m|n))\) for a certain space of differential operators \(\mathcal {D}'(m|n)\) indexed by a central element R of \(\mathcal {D}'(m|n) \otimes U(\mathfrak {gl}(m|n))\) . We then use this homomorphism to determine the image of Gelfand generators of the center of \(U(\mathfrak {gl}(m+1|n))\) . We achieve this by first relating \(\varphi _R\) to the corresponding Harish-Chandra homomorphisms and then using a super-analog of Newton’s formula for \(\mathfrak {gl}(m)\) relating Capelli generators and Gelfand generators. We also use the homomorphism \(\varphi _R\) to obtain representations of \(U(\mathfrak {gl}(m+1|n))\) from those of \(U(\mathfrak {gl}(m|n))\) , and find conditions under which these inflations are simple. Finally, we show that for a distinguished central element \(R_1\) in \(\mathcal {D}'(m|n)\otimes U(\mathfrak {gl}(m|n))\) , the kernel of \(\varphi _{R_1}\) is the ideal of \(U(\mathfrak {gl}(m+1|n))\) generated by the first Gelfand invariant \(G_1\) .
