Could someone please explain to me what the map, $g$, is doing intuitively?
$f:V\to V$ is a complex linear map and $f^n=\operatorname{id}$, for some $n>1$
$A$ is a subspace of $V$ and $f(A)\subset A$
$p:V\to A$ with $p|_A=\operatorname{id}_A$
$g:V\to A$ with $g(v)={1\over n}\sum_{k=0}^{n-1} f^k pf^{-k}(v)$
Thanks.