Bubbles in the affine Brauer and Kauffman categories
Representation Theory
2026-03-11 v2 Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.2408.07000,
title = {Bubbles in the affine Brauer and Kauffman categories},
author = {Alistair Savage and Ben Webster},
journal= {arXiv preprint arXiv:2408.07000},
year = {2026}
}
Comments
34 pages; v2: Significant edits, published version