Drinfeld realization of the elliptic Hall algebra

作者：Schiffmann Olivier^*

来源：Journal of Algebraic Combinatorics, 2012, 35(2): 237-262.

DOI：10.1007/s10801-011-0302-8

• Hall algebras
• Cherednik algebras
• Shuffle algebras
• Drinfeld new realization

We give a new presentation of the Drinfeld double epsilon of the (spherical) elliptic Hall algebra epsilon(+) 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).

• 出版日期2012-3