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Elliptic quantum groups

Giovanni Felder

Abstract

This note for the Proceedings of the International Congress of Mathematical Physics gives an account of a construction of an ``elliptic quantum group'' associated with each simple classical Lie algebra. It is closely related to elliptic face models of statistical mechanics, and, in its semiclassical limit, to the Wess-Zumino-Witten model of conformal field theory on tori.

Elliptic quantum groups

Abstract

This note for the Proceedings of the International Congress of Mathematical Physics gives an account of a construction of an ``elliptic quantum group'' associated with each simple classical Lie algebra. It is closely related to elliptic face models of statistical mechanics, and, in its semiclassical limit, to the Wess-Zumino-Witten model of conformal field theory on tori.

Paper Structure

This paper contains 4 theorems, 23 equations.

Key Result

Proposition 1

The function is a "unitary" weight zero solution of the modified Yang--Baxter equation, i.e., it is a generalized quantum $R$-matrix, with $\eta=\gamma/2$.

Theorems & Definitions (4)

  • Proposition 1
  • Theorem 2
  • Theorem 3
  • Theorem 4