## University of Sydney Algebra Seminar

# Jie Du (University of New South Wales)

## Friday 29 July, 12:05-12:55pm, Carslaw 175

### A double Hall approach to affine \(q\)-Schur algebras

I will talk about the structure of the double Ringel-Hall algebras associated with cyclic quivers and their connection with affine \(q\)-Schur algebras. This includes the Drinfeld-Jimbo type presentation, the quantum loop algebra interpretation, the affine quantum Schur-Weyl duality, the structure of affine \(q\)-Schur algebras and connections with various existing works by Lusztig, Schiffmann, Hubery, Varaganolo-Vasserot, McGerty, etc. I will also mention possible Beilinson-Lusztig-MacPherson type realization and Lusztig type integral forms. Representations of affine \(q\)-Schur algebras will probably be briefly discussed.

This is joint work with Bangming Deng and Qiang Fu.