is not of type ${\mathsf G}_2$, then the numbering is as follows: $$\begin{picture}(9000,1800)(2000,-900)
           \put(0,0){\multiput(0,0)(3600,0){2}{\circle*{150}}\thicklines\multiput(0,0)(2500,0){2}{\line(1,0){1100}}\multiput(1300,0)(400,0){3}{\line(1,0){200}}}
           \put(3600,0){\multiput(0,0)(3600,0){2}{\circle*{150}}\thicklines\multiput(0,0)(2500,0){2}{\line(1,0){1100}}\multiput(1300,0)(400,0){3}{\line(1,0){200}}}
           \put(7200,0){\multiput(0,0)(1800,0){2}{\circle*{150}}\thicklines\multiput(0,-60)(0,150){2}{\line(1,0){1800}}\multiput(1050,0)(-25,25){10}{\circle*{50}}\multiput(1050,0)(-25,-25){10}{\circle*{50}}}
           \put(9000,0){\multiput(0,0)(3600,0){2}{\circle*{150}}\thicklines\multiput(0,0)(2500,0){2}{\line(1,0){1100}}\multiput(1300,0)(400,0){3}{\line(1,0){200}}}
           \put(-150,-700){\tiny $\alpha_1$}
           \put(3450,-700){\tiny $\alpha_p$}
           \put(8850,-700){\tiny $\alpha_q$}
           \put(12450,-700){\tiny $\alpha_r$}
\end{picture}$$ The *little brother* of ${\lambda}$ with respect to ${\Delta}'$ is the dominant weight $${\lambda}_{{\Delta}'}^{\mathrm{lb}}= {\lambda}- \sum_{i=p}^q {\alpha}_i =
\left\{ \begin{array}{ll}
        {\lambda}-\omega_1+\omega_2 & \textrm{ if $G$ is of type $\sf{G}_2$} \\
        {\lambda}+ {\omega}_{p-1} - {\omega}_{p}  + {\omega}_{q+1} & \textrm{ otherwise}
\end{array} \right.$$ where ${\omega}_i$ is the fundamental weight associated to ${\alpha}_i$ if $1{\leqslant}i {\leqslant}r$, while ${\omega}_0 = {\omega}_{r+1} = 0$. The set of the little brothers of ${\lambda}$ will be denoted by ${\mathrm{LB}}({\lambda})$; notice that ${\mathrm{LB}}({\lambda})$ is empty if and only if ${\lambda}$ satisfies condition $(\star)$ of Theorem A. For convenience, define $\overline {\mathrm{LB}}({\lambda})={\mathrm{LB}}({\lambda})\cup\{{\lambda}\}$, while if ${\Delta}$ is connected and non-simply laced set ${\lambda}^{\mathrm{lb}}= {\lambda}_{\Delta}^{\mathrm{lb}}$.

\[lem:eta\] Assume $G$ to be simple and let ${\lambda}\in {\Lambda}^+{\smallsetminus}\{0\}$. Denote $\eta$ the highest root of $\Phi$ if the latter is simply laced or the highest short root otherwise.

1.  If ${\lambda}$ satisfies the condition $(\star)$ then $${V({{\lambda}})} \subset {V({\eta})} \otimes {V({{\lambda}})}.$$

2.  If ${\lambda}$ does not satisfy the condition $(\star)$ and if ${\lambda}^{\mathrm{lb}}$ is the little brother of ${\lambda}$ then $${V({{\lambda}})} \subset {V({\eta})} \otimes {V({{\lambda}^{\mathrm{lb}}})}.$$

If ${\Delta}$ is simply 