= Invertible tensor powers span the Schur algebra
{title2=$S(m,n)=\operatorname{span}\{g^{\otimes n}:g\in\operatorname{GL}(V)\}$}
The commutant of the <permutation> action on $V^{\otimes n}$ identifies with the <symmetric tensors> in $\operatorname{End}(V)^{\otimes n}$. <Polarization spanning of symmetric tensors> spans it by $a^{\otimes n}$. Interpolating $(a+tI)^{\otimes n}$ at $n+1$ values where $a+tI$ is invertible expresses each such power using invertible ones. Hence the <Schur algebra> is the linear span of the diagonal general linear action.
Back to article page
