Addendum to Olivier Schiffmann, "Drinfeld realization of the elliptic Hall algebra"

TL;DR

This paper extends Schiffmann's work by providing a Drinfeld realization of the elliptic Hall algebra, building on his previous presentation of its Drinfeld double, thus deepening the algebra's structural understanding.

Contribution

It offers a new Drinfeld realization of the elliptic Hall algebra, complementing Schiffmann's earlier presentation of its Drinfeld double.

Findings

Provides a Drinfeld realization for the elliptic Hall algebra

Builds on Schiffmann's presentation of the Drinfeld double

Enhances understanding of elliptic Hall algebra structure

Abstract

In \cite{S} O. Schiffmann gave a presentation of the Drinfel'd double of the elliptic Hall algebra which is similar in spirit to Drinfel'd's new realization of quantum affine algebras. Using this result together with a part of his proof we can provide such a description for the elliptic Hall algebra.