Bubbles in the affine Brauer and Kauffman categories

We introduce a generating function approach to the affine Brauer and Kauffman categories and show how it allows one to efficiently recover important sets of relations in these categories. We use this formalism to deduce restrictions on possible categorical actions and show how this recovers admissibility results that have appeared in the literature on cyclotomic Birman-Murakami-Wenzl (BMW) algebras and their degenerate versions, also known as cyclotomic Nazarov-Wenzl algebras or VW algebras.

💡 Research Summary

The paper develops a generating‑function formalism for the affine Brauer category (AB) and the affine Kauffman category (AK), providing a unified and streamlined way to handle the relations among cups, caps, crossings, dots, and bubbles that generate these diagrammatic monoidal categories. After recalling the standard presentations of AB (as in