  Let $W\subset O(V)$ be the Weyl group of a root system $R\subset V$. If
$a+b+c=0=a'+b'+c'$ with $a$, $b$ and $c$ respectively conjugated to $a'$, $b'$
and $c'$ in V , then $(a,b,c)$ is conjugated to $(a',b',c')$ in $V^3$ when each
projection of $a$ to an irreducible component of $V$ is co-linear to a
minuscule coweight.
