# Jie Du (University of New South Wales)

## q-Schur algebras and integral quantum affine gl(n)

Drinfeld’s new realisation of the quantum loop algebra of $$\mathfrak{gl}_n$$ does not offer naturally a Lusztig type form. We will show in this talk how affine q-Schur algebras and the Ringel-Hall algebras of cyclic quivers are used to reconstruct this quantum affine $$\mathfrak{gl}_n$$. In particular, we will show that the integral structures of both q-Schur algebras and Hall algebras give rise naturally to a Lusztig form for the quantum group. Further applications to the integral modified quantum groups and their canonical bases will also be discussed. This is joint work with Qiang Fu (and partially with Zhonghua Zhao).