English

Drinfeld realization of the elliptic Hall algebra

Quantum Algebra 2010-04-16 v1 Combinatorics

Abstract

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.

Keywords

Cite

@article{arxiv.1004.2575,
  title  = {Drinfeld realization of the elliptic Hall algebra},
  author = {Olivier Schiffmann},
  journal= {arXiv preprint arXiv:1004.2575},
  year   = {2010}
}

Comments

19 pages, lots of figures

R2 v1 2026-06-21T15:10:39.638Z