Anyonic Realization of $SU_q(N)$ Quantum Algebra

TL;DR

This paper demonstrates how a set of anyonic oscillators on a 2D lattice can realize the $SU_q(N)$ quantum algebra, linking the deformation parameter to anyonic statistics.

Contribution

It introduces a generalized Schwinger construction using anyonic oscillators to realize $SU_q(N)$ algebra, establishing a direct relation between the deformation parameter and anyonic statistics.

Findings

Realization of $SU_q(N)$ algebra via anyonic oscillators

Relation $q=exp(i\pi u)$ between deformation parameter and statistical parameter

Extension of algebraic structures to two-dimensional anyonic systems

Abstract

By considering a set of $N$ anyonic oscillators ( non-local, intrinsic two-dimensional objects interpolating between fermionic and bosonic oscillators) on a two-dimensional lattice, we realize the $SU_q(N)$ quantum algebra by means of a generalized Schwinger construction. We find that the deformation parameter $q$ of the algebra is related to the anyonic statistical parameter $\nu$ by $q=exp({\rm i}\pi\nu)$.