1,591 research outputs found
The braiding for representations of q-deformed affine
We compute the braiding for the `principal gradation' of for 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 in the deformation parameter . We also examine the convergence using probability, assuming a uniform
distribution for on the unit circle.Comment: LaTeX, 10 pages with 2 figs, uses epsfi
Making nontrivially associated modular categories from finite groups
We show that the non-trivially associated tensor category constructed from
left coset representatives of a subgroup of a finite group is a modular
category. Also we give a definition of the character of an object in a ribbon
category which is the category of representations of a braided Hopf algebra in
the category. The definition is shown to be adjoint invariant and
multiplicative. A detailed example is given. Finally we show an equivalence of
categories between the non-trivially associated double D and the category of
representations of the double of the group D(X).Comment: Approx 43 pages, uses LaTeX picture environmen
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