Young's rule
= Young's rule
{c}
{wiki}
Over the complex numbers,
$$
M^\lambda\cong\bigoplus_{\alpha\vdash n}
(S^\alpha)^{\oplus K_{\alpha\lambda}},
$$
where the <Kostka number> $K_{\alpha\lambda}$ counts semistandard tableaux of shape $\alpha$ and content $\lambda$. It is nonzero only when $\alpha$ dominates $\lambda$.