Braid group representations from a deformation of the harmonic oscillator algebra

TL;DR

This paper introduces a novel method to derive braid group representations using R-matrices from a quantum deformed harmonic oscillator algebra, focusing on lowest weight vectors to manage infinite-dimensional representations.

Contribution

It presents a new technique for constructing braid group representations from quantum deformed harmonic oscillator algebras, emphasizing lowest weight subspaces.

Findings

New braid group representations derived from quantum harmonic oscillator algebra

Technique applicable to infinite-dimensional representation spaces

Potential applications in topological quantum computing

Abstract

We describe a new technique to obtain representations of the braid group B_n from the R-matrix of a quantum deformed algebra of the one dimensional harmonic oscillator. We consider the action of the R-matrix not on the tensor product of representations of the algebra, that in the harmonic oscillator case are infinite dimensional, but on the subspace of the tensor product corresponding to the lowest weight vectors.