Rationality of Affine Vertex Operator Superalgebras with Rational Conformal Weights

For the affine vertex algebra $V_k(\mathfrak{g})$ at an admissible level $k$ of $\hat{\mathfrak{g}}$, we prove that certain subcategory weak $V_k(\mathfrak{g})$-module category is semisimple. As a consequence, show rational with respect to family Virasoro elements. We also operator superalgebras and minimal $W$-algebras are