Ultraproduct and oligomorphic-group constructions of interpolation categories for finite classical groups agree, and the categories depend only on a parameter t, with an additional parity label in the orthogonal case.
On representation categories of wreath products in non-integral rank
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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.
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Classical interpolation categories
Ultraproduct and oligomorphic-group constructions of interpolation categories for finite classical groups agree, and the categories depend only on a parameter t, with an additional parity label in the orthogonal case.