= Specht modules as minimal left ideals
{title2=$S^\lambda\cong\mathbb CS_nh_t$}
In the complex symmetric-group algebra, normalize a <Young symmetrizer> by $e_t=h_t/H_\lambda$. The <row-column collision lemma> proves $e_tAe_t=\mathbb Ce_t$, so $e_t$ is a <primitive idempotent> and $Ae_t$ is an irreducible left module. Different shapes are separated by the vanishing corner $h_\lambda A h_\mu=0$ for $\lambda>\mu$. Counting <conjugacy classes> then proves that these modules exhaust the <simple modules>.
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