Ordinary modules for affine vertex operator superalgebras

Let $\mathfrak{g}$ be a basic classical Lie superalgebra and let $\widehat{\mathfrak{g}}$ be the corresponding affine Lie superalgebra. In this paper, we first prove that a Cartan subalgebra acts semisimply on ordinary modules for the simple affine vertex operator superalgebra $L_{\widehat{\mathfrak