Consider a minuscule representation (in a semisimple case). This gives a decomposition:
g=p\oplus n. Is n commutative? 
(Sorry for a stupid question - I am not an expert and it's Sunday and I have no one to ask) 



Commutativity of nilpotents in minuscule case
$\mathfrak{n}$ is not well defined, it is better to speak about $\mathfrak{u}$, the unipotent radical of $\mathfrak{p}$. It is commutative in the COminuscule case.


