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arXiv · hep-th/0411243

The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group

Heng Fan·Bo-Yu Hou·Kang-Jie Shi·Rui-Hong Yue·Shao-You Zhao
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Abstract

In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation of the $A_{n-1}$ series elliptic quantum group given by Felder and Varchenko. The explicit dependence of elements of $L$-matrices on spectral parameter $z$ are given. They are of five different forms (A(1-4) and B). The algebra for the coefficients (which do not depend on $z$) are given. The algebra of form A is proved to be trivial, while that of form B obey Yang-Baxter equation (YBE). We also give the PBW base and the centers for the algebra of form B.

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Heng Fan, Bo-Yu Hou, Kang-Jie Shi, Rui-Hong Yue, Shao-You Zhao. 2004-11-26. The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group. https://doi.org/10.1063/1.1543635

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