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

TL;DR

This paper constructs a realization of the quantum affine Lie algebra U_q(A_N) using anyons on a 2D lattice, linking the deformation parameter to anyonic statistics, and recovers known fermionic structures in a specific limit.

Contribution

It introduces a novel anyonic realization of quantum affine Lie algebras, connecting lattice anyons with algebraic deformations and classical limits.

Findings

Realization of U_q(A_N) via lattice anyons

Relation between deformation parameter q and anyonic statistics

Recovery of classical affine Lie algebra in the limit q→1

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.