Drinfeld realization of the elliptic Hall algebra

Details Drinfeld realization of the elliptic Hall algebra Drinfeld realization of the elliptic Hall algebra

2010-04-15

arxiv.org/abs/1004.2575v1

Mathematics

Quantum Algebra

19 pages, lots of figures

Scientific paper

We give a new presentation of the Drinfeld double of the elliptic Hall algebra introduced in a previous work with I. Burban. 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 the groups GL(n) over a function field. It also provides proofs of some recent conjectures of Feigin, Feigin, Jimbo, Miwa and Mukhin.

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