‘Schur-Weyl duality’ is often used to describe a concept in representation theory involving two kinds of symmetry that determine each other. In its original form it goes back to Schur and Weyl (around 1930) and describes an important interplay between the representation theory of the general linear and the symmetric group over the complex numbers. In this talk we will describe some generalizations of this phenomenon with a focus on modern, still open or recently solved questions. In particular we are interested in situations, where the involved algebras are not semisimple. We will indicate the origin of filtrations, homological properties and hidden gradings on the involved algebras and applications to the representation theory of Lie superalgebras.
This video was produced by Syracuse University Department of Mathematics as part of ICRA 2016.
