Basic representations of quantum current algebras in higher genus

Benjamin Enriquez (1) , Stanislav Pakuliak (2) , Vladimir Rubtsov (3, 4)

1 IRMA - Institut de Recherche Mathématique Avancée
2 BLTP - Bogoliubov Laboratory of Theoretical Physics [Dubna]
3 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
4 Theory Division

We construct level 1 basic representations of the quantized current algebras associated to higher genus algebraic curves using one free field. We also clarify the relation between the elliptic current algebras of the papers [EF] and [JKOS].

Mots clés: Qantrum Group; Currents; Complex Curves; Projections; Representations

Domaines: Algèbres quantiques [math.QA]

Benjamin Enriquez, Stanislav Pakuliak, Vladimir Rubtsov. Basic representations of quantum current algebras in higher genus. 2005. ⟨hal-00009620⟩