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The affine VW supercategory. (English) Zbl 1455.18010

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).

MSC:

18M05 Monoidal categories, symmetric monoidal categories
17A70 Superalgebras
17B20 Simple, semisimple, reductive (super)algebras
33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
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