Braid group representations from a deformation of the harmonic oscillator algebra

Abstract

We describe a new technique to obtain representations of the braid group Bn 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.