On representation categories of wreath products in non-integral rank
arXiv:1105.5091 · doi:10.1016/j.aim.2012.05.002
Abstract
For an arbitrary commutative ring k and t in k, we construct a 2-functor S_t which sends a tensor category to a new tensor category. By applying it to the representation category of a bialgebra we obtain a family of categories which interpolates the representation categories of the wreath products of the bialgebra. This generalizes the construction of Deligne's category Rep(S_t,k) for representation categories of symmetric groups.
[v3] 41 pages, appendix added; final version [v2] 39 pages, title changed [v1] 32 pages