REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: Starting from a graded Frobenius superalgebra B, we consider a graphical calculus of B-decorated string diagrams. From this calculus we produce algebras consisting of closed planar diagrams and of closed annular diagrams. The action of annular diagrams on planar diagrams can be used to make clockwise (or counterclockwise) annular diagrams into an inner product space. I will explain how this gives a graphical realization of the space of symmetric functions equipped with the Jack inner product. This is joint work with Tony Licata and Alistair Savage.