Drinfeld realization of the elliptic Hall algebra
نویسنده
چکیده
We give a new presentation of the Drinfeld double E of the (spherical) elliptic Hall algebra 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) 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).
منابع مشابه
Wakimoto realization of Drinfeld current for the elliptic quantum algebra U q , p ( ŝl 3 ) December 4 , 2008
We study a free field realization of the elliptic quantum algebra Uq,p(ŝl3) for arbitrary level k. We give the free field realization of elliptic analogue of Drinfeld current associated with Uq,p(ŝl3) for arbitrary level k. In the limit p → 0, q → 1 our realization reproduces Wakimoto realization for the affine Lie algebra ŝl3. PACS numbers : 02.20.Sv, 02.20.Uw, 02.30.Ik
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تاریخ انتشار 2012