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arXiv · hep-th/0003201

The braiding for representations of q-deformed affine $sl_2$

E. J. Beggs·P. R. Johnson
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Abstract

We compute the braiding for the `principal gradation' of $U_q(\hat{{\it sl}_2})$ for $|q|=1$ from first principles, starting from the idea of a rigid braided tensor category. It is not necessary to assume either the crossing or the unitarity condition from S-matrix theory. We demonstrate the uniqueness of the normalisation of the braiding under certain analyticity assumptions, and show that its convergence is critically dependent on the number-theoretic properties of the number $τ$ in the deformation parameter $q=e^{2πiτ}$. We also examine the convergence using probability, assuming a uniform distribution for $q$ on the unit circle.

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E. J. Beggs, P. R. Johnson. 2000-03-22. The braiding for representations of q-deformed affine $sl_2$. https://doi.org/10.1063/1.1357197

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