Schur-Weyl duality and its generalizations

Schur-Weyl duality was originally defined by Schur in 1901, which builds a correspondence between the representations of the symmetric group and the polynomial representations of the general linear group. In this talk, I will first walk through the classical Schur-Weyl duality, which states that the symmetric group and the general linear group generate each other’s centralizers. Then I will discuss some possible generalizations of the classical Schur-Weyl duality, for example, the duality between the orthogonal group and the Brauer algebra.