Licata, AnthonyRosso, DanieleSavage, Alistair2021-05-130097-3165http://hdl.handle.net/1885/232984Starting 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. Our main theorem identifies this space with the space of symmetric functions equipped with the Jack inner product at Jack parameter dim⁡Beven−dim⁡Bodd. In this way, we obtain a graphical realization of that inner product space.The first author was supported by Discovery Project grant DP140103821 from the Australian Research Council. The third author was supported by Discovery Grant RGPIN-2017-03854 from the Natural Sciences and Engineering Research Council of Canada.application/pdfen-AU© 2017 Elsevier Inc.Symmetric functionsJack inner productCategorificationHeisenberg algebraGraded Frobenius superalgebraFock spaceWreath product algebra2018-0410.1016/j.jcta.2017.11.0202020-11-23