Bubbles in the affine Brauer and Kauffman categories
Alistair Savage, Ben Webster
TL;DR
This paper introduces a generating function method for affine Brauer and Kauffman categories, enabling efficient relation recovery and revealing restrictions on categorical actions, thus connecting to cyclotomic BMW and Nazarov-Wenzl algebras.
Contribution
It presents a novel generating function formalism that simplifies relation derivation and clarifies restrictions on categorical actions in affine Brauer and Kauffman categories.
Findings
Efficient relation recovery in affine categories
Restrictions on categorical actions derived
Connections to cyclotomic BMW and Nazarov-Wenzl algebras
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.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Geometry and complex manifolds · Algebraic Geometry and Number Theory