Schur-Weyl duality (GL(n) / S_k commutant on (C^n)^{tensor k})

Schur-Weyl duality (Schur 1901 dissertation; Weyl 1939 *Classical Groups*) states that on the k-fold tensor power V^{tensor k} of an n-dimensional complex vector space, the action of the general linear group GL(n) and the symmetric group…