  In their study of characters of minimal affinizations of representations of
orthogonal and symplectic Lie algebras, Chari and Greenstein conjectured that
certain Jacobi-Trudi determinants satisfy an alternating sum formula. In this
note, we prove their conjecture and slightly more. The proof relies on some
symmetries of the ring of symmetric functions discovered by Koike and Terada.
Using results of Hernandez, Mukhin-Young, and Naoi, this implies that the
characters of minimal affinizations in types B, C, and D are given by a
Jacobi-Trudi determinant.
