Anyons and Quantum Groups

Abstract

Anyonic oscillators with fractional statistics are built on a two-dimensional square lattice by means of a generalized Jordan-Wigner construction, and their deformed commutation relations are thoroughly discussed. Such anyonic oscillators, which are non-local objects that must not be confused with $q$-oscillators, are then combined à la Schwinger to construct the generators of the quantum group $SU(2)_q$ with $q=\exp({\rm i}πν)$, where $ν$ is the anyonic statistical parameter.