Geodesic
Drinfeld realization of the elliptic Hall algebra
Journal of Algebraic Combinatorics, Tome 35 (2012) no. 2, pp. 237-262.

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Summary: We give a new presentation of the Drinfeld double $E$ boldsymbol$\mathcal $E of the (spherical) elliptic Hall algebra $E ^{+}$ boldsymbolmathcalE^+ 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) Eisenstein series for $GL( n)$ over a function field. It also provides proofs of some recent conjectures of Feigin, Feigin, Jimbo, Miwa and Mukhin ( arXiv:1002.3100, 2010).
Keywords: keywords Hall algebras, Cherednik algebras, shuffle algebras, Drinfeld new realization 
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     author = {Schiffmann, Olivier},
     title = {Drinfeld realization of the elliptic {Hall} algebra},
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Schiffmann, Olivier. Drinfeld realization of the elliptic Hall algebra. Journal of Algebraic Combinatorics, Tome 35 (2012) no. 2, pp. 237-262. http://geodesic.mathdoc.fr/item/JAC_2012__35_2_a4/