Indecomposable objects in Khovanov-Sazdanovic’s generalizations of Deligne’s interpolation categories

New preprint.


We discuss categorical tools for the classification problem of indecomposable objects in Karoubian tensor categories. These tools include: filtrations, gradings, field extensions and Galois descent for such categories. We apply these tools to Khovanov-Sazdanovic’s recent generalizations of Deligne’s interpolation categories. Our chosen categorical point of view allows us to deduce results with a high level of generality: for example, we are able to determine the graded Grothendieck ring of Deligne’s interpolation categories over arbitrary fields, and the case of positive characterstic provides a natural setup for symmetric functions in the modular case.