Nakai–Nakanishi conjecture for type C_n tableau formulas

Let $\mathfrak{g}$ be of type $C_n$, let $\lambda/\mu$ be a skew diagram, and let $\chi_{\lambda/\mu,a}$ be the associated Jacobi–Trudi determinant for $a\in\mathbb{C}$. Let $\operatorname{Tab}(C_n,\lambda/\mu)$ be the set of tableaux defined by the paper's tableau conditions, and let the corresponding tableau expression be the right-hand side of the equality referred to as

. **Nakai–Nakanishi's tableau conjecture.** For any skew diagram $\lambda/\mu$ satisfying $l(\lambda')=2$ and $l(\lambda)\le n+1$, the equality

holds. This extends the tableau rule established in the paper beyond the cases directly derived there; the supplied text gives no resolution of this conjecture.