= Kernel intersection theorem for Specht modules
{title2=$S^\lambda=\bigcap_{i,v}\ker\psi_{i,v}$}
For a <partition of an integer> $\lambda$, let $\psi_{i,v}:M^\lambda\to M^{\lambda(i,v)}$ sum all <tabloids> obtained by retaining $v$ elements of row $i+1$ and moving its other $\lambda_{i+1}-v$ elements into row $i$, leaving the other row sets unchanged. Here $0\le v<\lambda_{i+1}$ and $\lambda(i,v)$ replaces $(\lambda_i,\lambda_{i+1})$ by $(\lambda_i+\lambda_{i+1}-v,v)$; <Young permutation modules> are defined for compositions too. Then $S^\lambda=\bigcap_{i,v}\ker\psi_{i,v}$ over every <field>. Pairwise column cancellation gives inclusion of the <Specht module> in each kernel. The reverse inclusion follows by straightening the <tabloid> coefficients using these adjacent-row relations: the remaining free leading coefficients are exactly those of the <standard polytabloid basis>.
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