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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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up vote 2 down vote accepted

$\mathfrak{n}$ 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.

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