Anyonic Realization of the Quantum Affine Lie Algebras
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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 $ν$ of the anyons by $q = e^{iπν}$. In the limit of the deformation parameter going to one we recover the Feingold-Frenkel fermionic construction of undeformed affine Lie algebras.
8p, LaTeX, subeqn.sty. Also available at http://lapphp0.in2p3.fr/preplapp/psth/anyon_ac.ps.gz
8p, LaTeX, subeqn.sty. Also available at http://lapphp0.in2p3.fr/preplapp/psth/anyon_ac.ps.gz