The elliptic Hall algebra has appeared in many different contexts in representation theory and geometry under different names. We will explain how this algebra is categorified by the quantum Heisenberg category, which is a diagrammatic category modelled on affine Hecke algebras. This categorification can be used to construct large families of representations for the elliptic Hall algebra.
This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.
