The Spin Brauer Category - Extending Representation Theory

Explore a comprehensive lecture on the spin Brauer category presented by Alistair Savage from the University of Ottawa's Mathematics & Statistics department. Delve into the intricacies of this diagrammatic monoidal category that expands upon the traditional Brauer category by incorporating the crucial spin representation. Discover how this new spin Brauer category addresses the limitations of its predecessor in describing the representation theory of orthogonal and symplectic groups. Examine the role of Brauer algebras as endomorphism algebras and their significance in orthogonal and symplectic analogues of Schur-Weyl duality. Gain insights into the collaborative research conducted with Peter McNamara, which aims to provide a more complete picture of these mathematical structures. Recorded at the Institute for Pure & Applied Mathematics (IPAM) Symmetric Tensor Categories and Representation Theory Workshop, this 50-minute talk offers a deep dive into advanced concepts in algebraic representation theory.