The conformal block inequality for symmetric divisors on \overline{M}_{0,9}

Let $\mathfrak{g}$ be a simple Lie algebra. Let $D:=\operatorname{Sym} D(\mathfrak{g},\ell,\vec{\lambda})$ be a symmetrized conformal block divisor on $\overline{M}_{0,9}$ associated to $\mathfrak{g}$. The conformal block inequality. The divisor $D$ satisfies

$$D \cdot F_{6,1,1,1} \leq 3D \cdot F_{5,2,1,1}.$$

In particular, conformal block divisors do not cover the symmetric nef cone of $\overline{M}_{0,9}$.