The Brauer category is a diagrammatic monoidal category describing the representation theory of the orthogonal and symplectic groups. Its endomorphism algebras are Brauer algebras, which replace the group algebra of the symmetric group in the orthogonal and symplectic analogues of Schur-Weyl duality. However, the Brauer category is missing one important piece of the picture—the spin representation. We will introduce a larger category, the spin Brauer category, that remedies this deficiency. This is joint work with Peter McNamara.
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