The braiding for representations of q-deformed affine $s{l}_2$

Abstract

We compute the braiding for the `principal gradation' of $U_q(\widehat{{sl}_2})$ 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.

LaTeX, 10 pages with 2 figs, uses epsfig

References in corpus (2)

• Inverse scattering and solitons in $A_{n-1}$ affine Toda field theories
• Exact quantum S-matrices for solitons in simply-laced affine Toda field theories