Let $W$ be a Weyl group, let $\mu$ be an antidominant weight. Let $W_I$ be the Weyl group generated by $I$ and $w_I$ be the longest element in $W_I$. Denote ${}^IW$ the set of minimal length coset representative of $W_I\backslash W$.
Given $w_Iw\le w_Iw'$, $x,w,w'\in {}^IW$, does it implies $\dim \text{Ext}^i_{\mathcal{O}^\mathfrak{p}}(M_I(w_Ix\cdot \mu),L(w_Iw\cdot \mu))\le \dim \text{Ext}^i_{\mathcal{O}^\mathfrak{p}}(M_I(w_Ix\cdot \mu),L(w_Iw'\cdot \mu))$?
