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arXiv · hep-th/9511013

Anyonic Realization of the Quantum Affine Lie Algebra U_q(A_N)

L. Frappat·A. Sciarrino·S. Sciuto·P. Sorba
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Abstract

We give a realization of quantum affine Lie algebra $U_q(\hat A_{N-1})$ in terms of anyons defined 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 algebra.

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L. Frappat, A. Sciarrino, S. Sciuto, P. Sorba. 1995-11-02. Anyonic Realization of the Quantum Affine Lie Algebra U_q(A_N). https://doi.org/10.1016/0370-2693(95)01518-3

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