## University of Sydney Algebra Seminar

# Jie Du (UNSW)

## Friday 7th March, 12:05-12:55pm, Place: Carslaw 373

### Quantum affine gl_n via Hecke algebras

By presenting the quantum loop algebra of $gl_n$ as the double Hall algebra associated with a cyclic quiver, we will construct a new basis together with explicit multiplication formulas of a basis element by a generator. In this way, we obtain an affine generalisation of the realisation of quantum $gl_n$ by Beilinson, Lusztig and MacPherson. In contrast to their geometric approach, our construction is purely algebraic and combinatorial. As applications, I will also talk about their integral form and modified version. This is joint work with Qiang Fu.