Let $(V,h)$ be a Hermitian [vector space](/page/Vector%20Space) of complex dimension $n$, let $V_{\mathbb R}$ denote the underlying real vector space, and let $J:V_{\mathbb R}\to V_{\mathbb R}$ be the complex structure. Let $g:=\operatorname{Re}h$ be the associated real [inner product](/page/Inner%20Product), and define the real-valued Kähler form $\omega\in \Lambda^2(V_{\mathbb R}^*)$ by
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\begin{align*}
\omega(u,v)=g(Ju,v)
\end{align*}
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for all $u,v\in V_{\mathbb R}$. For each degree $k\in\{0,\dots,2n\}$, set
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\begin{align*}
E_k:=\Lambda^k(V_{\mathbb R}^*)\otimes_{\mathbb R}\mathbb C
\end{align*}