Jose Simental Rodriguez (Universidad Nacional Autónoma de México and ICERM): The elliptic Hall algebra and the double Dyck path algebra

Title:  The elliptic Hall algebra and the double Dyck path algebra

Abstract:  The double Dyck path algebra was initially defined by Carlsson and Mellit as an important technical tool in their proof of the shuffle conjecture. It is a non-unital algebra with enough idempotents that contains all type A affine Hecke algebras simultaneously, together with raising and lowering operators that move between them. I will define this algebra and describe in precise terms its relationship to the elliptic Hall algebra. Time permitting, I will also deal with the representation theory of the double Dyck path algebra, in particular recovering the "semi-infinite" representations of the elliptic Hall algebra defined by Feigin-Feigin-Jimbo-Miwa-Mukhin. This is based on joint works with Nicolle González and Eugene Gorsky.