Braid group representations from a deformation of the harmonic oscillator algebra

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...

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Bibliographic Details
Published in:arXiv.org 2016-10
Main Author: Tarlini, Marco
Format: Article
Language:English
Subjects:
Algebra
Braid theory
Deformation
Harmonic oscillators
Mathematical analysis
Oscillators
Representations
Tensors
Vectors (mathematics)
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1610.04409