Quantum groups in higher genus and Drinfeld's new realizations method ($sl_{2}$ case)

B. Enriquez; V. Rubtsov

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arXiv · q-alg/9601022

Quantum groups in higher genus and Drinfeld's new realizations method ($sl_{2}$ case)

B. Enriquez·V. Rubtsov

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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 $sl_{2}$ case, adapting Drinfeld's ``new realizations'' technique. We study finite dimensional representations of these algebras in level $0$, and some elliptic examples.

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B. Enriquez, V. Rubtsov. 1996-01-21. Quantum groups in higher genus and Drinfeld's new realizations method ($sl_{2}$ case). https://arxiv.org/abs/q-alg/9601022

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