On minimal singular vectors of V^κ(g) for types B and C

Let g be a finite-dimensional simple Lie algebra of type B or C over C. Given κ∈ C, let V^κ(g) be the universal affine vertex algebra associated with g at level $κ$. We characterize the weights of minimal singular vectors of V^κ(g) with respect to the generalized Cartan matrix, when V^κ(g) is not simple and $κ$ is not critical. Furthermore, we determine the corresponding longest Weyl elements in the Kashiwara-Tanisaki character theorem of the singular vectors.