= Schur–Weyl duality
{c}
{title2=$V^{\otimes n}=\bigoplus_{\lambda\vdash n}S^\lambda\otimes D_\lambda(V)$}
{wiki}
The commuting actions of the <symmetric group> and the <general linear group> on a <tensor power> are mutual <commutants>. The displayed sum ranges over partitions with at most $\dim V$ rows. The <Specht modules> and <Schur modules> are the simple factors for the two actions. In particular a primitive <Young symmetrizer> selects one copy of the matching Schur <module>.
Back to article page
