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Conformal field theory and integrable systems associated to elliptic curves. (English) Zbl 0852.17014

Chatterji, S. D. (ed.), Proceedings of the international congress of mathematicians, ICM ’94, August 3-11, 1994, Zürich, Switzerland. Vol. II. Basel: Birkhäuser. 1247-1255 (1995).
The author defines an “elliptic quantum group”, starting with a certain solution of (a generalisation of) the quantum Yang-Baxter equation depending on theta functions, and using the standard construction due to the St. Petersburg school. This elliptic quantum group is an analogue of Yangians and quantum affine algebras, which would by obtained by the same construction starting from rational or trigonometric solutions of the quantum Yang-Baxter equation, respectively.
For the entire collection see [Zbl 0829.00015].

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
14H52 Elliptic curves
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