= Young symmetrizer
{c}
{title2=$h_t=c_tr_t$}
{wiki}
For a <Young tableau> $t$, let $r_t$ sum its row permutations and $c_t$ be the signed sum of its column permutations in the <group algebra> of the <symmetric group>. The product $h_t=c_tr_t$ is a Young symmetrizer. The other order is another conventional realization. It satisfies $h_t^2=H_\lambda h_t$, where $H_\lambda$ is the <hook product of a partition>, so division by that scalar gives a primitive <idempotent> in characteristic zero. Acting on a <tensor power> constructs a <Schur module>.
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