= Injectivity of powers of the Lefschetz operator
{title2=$L^r:\mathcal A^k\hookrightarrow\mathcal A^{k+2r}\quad(r+k\le n)$}
The <Hermitian Lefschetz operator> has injective powers in the indicated range. The <commutator formula for powers of the Lefschetz operator> proves this by induction on $r+k$: a form in the kernel can be written as $L\alpha$ using injectivity of the smaller power, and the lower-degree form $\alpha$ is then in the kernel of another power covered by the induction hypothesis.
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