# $SU(n)$-invariant subring of $\Lambda^{*}\mathbb{R}^{2n}$

I have the following question: Let $R \subset \Lambda^{*}\mathbb{R}^{2n}$ be the sub-ring of forms which are preserved by $SU(n)$. How can one show that this subring is generated by $\Omega_{0}$ and $\omega_0$ where $\Omega_{0}=dz^{1}\wedge ... \wedge dz^{n}$ and $\omega_{0}=\frac{i}{2}\sum_{i=1}^{n}dz^{i}\wedge d\overline{z}^{i}$?

monica

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does any one have an idea? –  monica Feb 9 '13 at 5:47