I will present results of joint work with T. Arakawa, on representation theory of simple affine W-algebras. For so-called exceptional W-algebras, the category of representations acquires the structure of a modular tensor category, and in this talk I will describe the modular data and fusion rules for some cases. In many cases the modular data matches that of quantum groups at roots of unity, but in other cases, the results are quite mysterious.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Geometric Representation Theory and W-algebras.
