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)
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$\mathfrak{n}$ 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. 

