4 problems

Suppose that $\mathfrak{g}$ is of type $B_n$, $C_n$ or $D_{n+1}$ and that $\lambda\in P^+$ satisfies $\lambda(h_i)=0$ for $i\ge n$. Let $\Psi_\lambda$ be the root subset defined fr…

Let $\lie g$ be of type $D$ or $E$, with the decomposition used in the paper into subdiagrams $I_1$, $J$, and $I_2$, where $J$ is of type $D_4$. Let $\lambda\in P^+$ and let…

Let $\lie g$ be of type $D$ or $E$, let $i_0$ be its unique triply connected node, and let $\lambda\in P^+$ be supported on the three connected components of $I\setminus\{i_0\}$. F…

Let $\lambda\in P^+$ be such that its extended support $\overline{\operatorname{supp}}(\lambda)$ does not contain a subdiagram of type $D_4$. Let…