Commutator formula for powers of the Lefschetz operator
= Commutator formula for powers of the Lefschetz operator
{title2=$[L^r,\Lambda]|_{\mathcal A^k}=r(k-n+r-1)L^{r-1}$}
For the <Hermitian Lefschetz operator> on a complex $n$-manifold, the <Lefschetz commutator> and the <commutator derivation identity> imply this formula. When expanding a product commutator, one must evaluate $[L,\Lambda]$ on the degree after the powers of $L$ to its right have acted.