On representation categories of wreath products in non-integral rank

TL;DR

This paper introduces a 2-functor that interpolates representation categories of wreath products of bialgebras over arbitrary rings, generalizing Deligne's categories for symmetric groups.

Contribution

It constructs a new 2-functor S_t that extends representation categories to non-integral ranks, broadening the scope of categorical interpolation.

Findings

Defines a 2-functor S_t for tensor categories.

Interpolates wreath product representation categories.

Generalizes Deligne's Rep(S_t,k) for symmetric groups.

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.