Title: The structure and representation theory of quantum toroidal algebras
Speaker: Duncan Laurie (University of Oxford, UK)
Date: 08 December 2023
Time: 3 pm
Venue: LH-3, Mathematics Department
Quantum toroidal algebras are the next class of quantum affinizations after quantum affine algebras, and can be thought of
as “double affine quantum groups”. However, surprisingly little is known thus far about their structure and representation
theory in general.
In this talk we’ll start with a brief recap on quantum groups and the representation theory of quantum affine algebras. We
shall then introduce and motivate quantum toroidal algebras, before presenting some of the known results. In particular, we
shall sketch our proof of a braid group action, and generalise the so-called Miki automorphism to the simply laced case.
Time permitting, we shall discuss future directions and applications including constructing representations of quantum toroidal
algebras combinatorially, written in terms of Young columns and Young walls.