The affine VW supercategory (Q2310816)

In the article under review, the authors introduce two linear monoidal supercategories: the Brauer supercategory \(s\mathcal{B}r\) and the affine VW (or Nazarov-Wenzl) supercategory. The main result of this work is to provide explicit bases for their morphism spaces (see Theorems 1 and 2). This is proved in two steps. The first one consists in showing that the given sets span the corresponding morphism spaces, by a topological argument (see Proposition 11 and 12). Secondly, they prove that the previous sets are linearly independent (see Sections 4.10 and 4.11). Finally, as an application, in Section 5 they describe the center of the associated endomorphism algebras of the affine VW supercategory (see Theorem 53).