= Solution
The <symmetric group> acts transitively on the <Young tableaux> of a fixed shape. Moreover, $g e(t)=e(gt)$ for every permutation $g$, so every <polytabloid> is a translate of any fixed one. Hence the <Specht module> is a <cyclic module> generated by $e(t)$.
It remains to see that $e(t)\ne0$. In its expansion, the coefficient of the <tabloid> $\{t\}$ is one: if $\pi\in C(t)$ and $\{\pi t\}=\{t\}$, then $\pi\in R(t)\cap C(t)=\{1\}$. Thus the generator, and therefore the module, is nonzero.
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