= Young-symmetrizer tensor decomposition
{c}
{title2=$V^{\otimes n}=\bigoplus_{\lambda,t\ \mathrm{standard}}h_tV^{\otimes n}$}
The standard-tableau right-ideal decomposition of $\mathbb CS_n$, tensored over that algebra with $V^{\otimes n}$, gives this direct sum of <general linear group> <modules>. With $e_t=h_t/H_\lambda$, the map $e_t\mathbb CS_n\otimes T\to e_tT$ is an isomorphism. Individual summands generally need not be <symmetric group> <submodules>; instead each is a <Schur module> for the commuting action.
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