Graduate Algebra Symposium
Gordon Brown
The Marked Brauer Category and Modules of Lie Superalgebras
The original Brauer algebra generalized the role of the general linear group in Schur-Weyl duality, affording us more information about the representation theory of the orthogonal group. Generalizing further by adding extra structure (including "markings" and a grading) to the inherent Brauer diagrams furnishes a functor between the category whose hom-spaces are these new diagrams and a certain subcategory of modules of a Lie superalgebra. In this talk I discuss a recent paper of Kujawa and his student Tharp, in which they utilize this process to provide sufficient conditions for the functor to be full and faithful when the underlying field is the complex numbers.