Anyonic Realization of the Quantum Affine Lie Algebras

Abstract

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 $\nu$ 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.

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References in corpus (1)

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

Cited by in corpus (2)

• Anyonic Realization of the Quantum Affine Lie Superalgebra U_q(A(M,N)^{(1)})
• Fractional spin through quantum affine algebras with vanishing central charge