The braiding for representations of q-deformed affine sl2sl_2

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.Comment: LaTeX, 10 pages with 2 figs, uses epsfi

Stochastic Evolution with Slow Learning..

This paper studies the extent to which diffusion approximations provide a reliable guide to equilibrium selection results in finite games. It is shown that they do for a class of finite games with weak learning provided that limits are taken in a certain order. The paper also shows that making mutation rates small does not in general select a unique equilibrium but making selection strong does.