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

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 $\nu$ 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 algebra.

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