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

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

2004-11-26

arxiv.org/abs/hep-th/0411243v1

J. Math. Phys. 44 1276-1296 (2003)

Physics

High Energy Physics

High Energy Physics - Theory

23 pages

Scientific paper

10.1063/1.1543635

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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