Quantum Schur algebras and their affine and super cousins

Abstract:

Schur algebras are certain finite dimensional algebras introduced by Issai Schur, one of the pioneers of representation theory, at the beginning of last century to relate representations of the general linear and symmetric groups. This theory is also known as Schur-Weyl duality. Over its history of more than one hundred years, Schur algebras continue to make profound influence in several areas of mathematics such as Lie theory, representation theory, invariant theory, combinatorics, etc. I will outline some definitions of quantum Schur algebras and discuss a number of applications. In particular, I will report on the latest developments in the affine and super case.