Let $(V,h)$ be a Hermitian [vector space](/page/Vector%20Space) of complex dimension $n$, let $J:V_{\mathbb R}\to V_{\mathbb R}$ be its complex structure, and let $V_{\mathbb R}$ be the underlying real vector space. Let $\omega\in \Lambda^2 V_{\mathbb R}^*$ be the associated Kähler form, defined by
Write $L$ for the resulting degree-$2$ operator on $E$, and write $L^q:E^j\to E^{j+2q}$ for its $q$-fold iterate when $q\ge 0$. Then, for every integer $k$ with $0\le k\le n$, the map