Solution
= Solution
The <symmetric group> acts transitively on the <Young tableau>[tableaux] of a fixed shape. Thus every $s\in\Delta^\lambda$ is $g t$ for some $g\in S_n$, and the definition of a <polytabloid> gives
$$
e(s)=e(gt)=g e(t).
$$
Since the <Specht module> is spanned by all $e(s)$, it is the cyclic $\mathbb F S_n$-module generated by $e(t)$.