Quantum groups in higher genus and Drinfeld's new realizations method ($s{l}_2$ case)

Abstract

We define double (central and cocentral) extensions of Manin pairs introduced by Drinfeld, attached to curves and meromorphic differentials. We define ``infinite twistings'' of these pairs and quantize them in the $s{l}_2$ case, adapting Drinfeld's ``new realizations'' technique. We study finite dimensional representations of these algebras in level $0$, and some elliptic examples.

21 pages