Anyonic Realization of the Quantum Affine Lie Algebras

Details Anyonic Realization of the Quantum Affine Lie Algebras Anyonic Realization of the Quantum Affine Lie Algebras

1996-07-18

arxiv.org/abs/q-alg/9607023v1

Czech.J.Phys.47:5-12,1997

Physics

High Energy Physics

High Energy Physics - Theory

8p, LaTeX, subeqn.sty. Also available at http://lapphp0.in2p3.fr/preplapp/psth/anyon_ac.ps.gz

Scientific paper

10.1023/A:1021479625167

We give a realization of the quantum affine Lie algebras $\uqa$ and $\uqc$ in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter $q$ being related to the statistical parameter $\nu$ of the anyons by $q = e^{i\pi\nu}$. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel fermionic construction of undeformed affine Lie algebras.

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