Anyonic Construction of the $SL_{Q,s}(2)$ Algebra

TL;DR

This paper constructs the quantum semi-group $sl_{(q,s)}(2)$ using anyonic oscillators on a 2D lattice, linking algebra parameters to statistical and oscillator deformation parameters.

Contribution

It introduces a novel realization of the $sl_{(q,s)}(2)$ algebra via anyonic oscillators and a generalized Schwinger construction, connecting algebraic parameters to physical properties.

Findings

Established a connection between algebra parameter q and anyonic statistics

Linked parameter s to a deformed oscillator at each lattice point

Provided a new algebraic framework for anyonic systems

Abstract

Considering anyonic oscillators in a two-dimensional lattice, we realize the quantum semi-group $sl_{(q,s)}(2)$ by means of a generalized Schwinger construction. We find that the parameter $q$ of the algebra is connected to the statistical parameter, whereas the $s$ parameter is related to a $s$-deformed oscillator introduced at each point of the lattice.