Let $(X,\omega)$ be a Kähler manifold of complex dimension $n$, let $(L,h)$ be a Hermitian holomorphic line bundle on $X$, and let $x\in X$. Let $(\zeta_1,\dots,\zeta_n)$ be a unitary coframe of the holomorphic cotangent space at $x$ such that
for [real numbers](/page/Real%20Numbers) $\lambda_1,\dots,\lambda_n$.
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Let $\Lambda_\omega$ denote contraction by $\omega$ at $x$, and let $i\Theta(L,h)_x$ act on $L_x$-valued forms by exterior multiplication in the form factor. With the commutator convention
the operator $[i\Theta(L,h),\Lambda_\omega]$ acts diagonally on the standard basis
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\begin{align*}
\zeta_I\wedge \overline{\zeta_J}\otimes e
\end{align*}
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of the [vector space](/page/Vector%20Space) of $L_x$-valued $(p,q)$-forms at $x$, where $0\le p,q\le n$, $e\in L_x\setminus\{0\}$, $I,J\subset\{1,\dots,n\}$ are increasing index sets with $|I|=p$ and $|J|=q$, and, for $I=\{i_1<\cdots<i_p\}$ and $J=\{j_1<\cdots<j_q\}$,