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

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

2000-03-22

arxiv.org/abs/hep-th/0003201v1

J.Math.Phys. 42 (2001) 2156-2166

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 10 pages with 2 figs, uses epsfig

Scientific paper

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 $\tau$ in the deformation parameter $q=e^{2\pi i\tau}$. We also examine the convergence using probability, assuming a uniform distribution for $q$ on the unit circle.

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