Anyonic Realization of the Quantum Affine Lie Algebras
Résumé
We give a realization of the quantum affine Lie algebras ${\cal U}_q(A_N^{(1)})$ and ${\cal U}_q(C_N^{(1)})$ 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.