Anyonic Realization of the Quantum Affine Lie Algebra Uq(AN)
Abstract
We give a realization of quantum affine Lie algebra Uq( AN-1) in terms of anyons defined on a two-dimensional lattice, the deformation parameter q being related to the statistical parameter of the anyons by q = eiπ. 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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