= Trace computation of Specht module dimension
{title2=$\dim S^\lambda=n!/H_\lambda$}
Right multiplication by $e_t=h_t/H_\lambda$ on the <group algebra> is an <idempotent> with image $Ae_t$. Every diagonal entry in the <permutation> basis is the coefficient of the identity in $e_t$, namely $1/H_\lambda$. Thus its rank equals its trace, giving $\dim S^\lambda=n!/H_\lambda$. Triangular standard-tableau ideals and the <Robinson–Schensted correspondence> identify this dimension with the standard-tableau count.
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