# Drinfeld realization of the elliptic Hall algebra

@article{Schiffmann2010DrinfeldRO,
title={Drinfeld realization of the elliptic Hall algebra},
author={Olivier Schiffmann},
journal={Journal of Algebraic Combinatorics},
year={2010},
volume={35},
pages={237-262}
}
• O. Schiffmann
• Published 15 April 2010
• Mathematics
• Journal of Algebraic Combinatorics
We give a new presentation of the Drinfeld double $\boldsymbol{\mathcal {E}}$ of the (spherical) elliptic Hall algebra $\boldsymbol{\mathcal{E}}^{+}$ introduced in our previous work (Burban and Schiffmann in Duke Math. J. preprint math.AG/0505148, 2005). This presentation is similar in spirit to Drinfeld’s ‘new realization’ of quantum affine algebras. This answers, in the case of elliptic curves, a question of Kapranov concerning functional relations satisfied by (principal, unramified…
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Addendum to: Olivier Schiffmann, “Drinfeld realization of the elliptic Hall algebra”
In (J. Algebr. Comb. doi:10.1007/s10801-011-0302-8, 2011), O. Schiffmann gave a presentation of the Drinfeld double of the elliptic Hall algebra which is similar in spirit to Drinfeld’s new
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