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A graphical calculus for the Jack inner product on symmetric functions

Licata, Anthony; Rosso, Daniele; Savage, Alistair


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. Our main theorem identifies this space with the space of symmetric functions equipped with the Jack inner product at Jack...[Show more]

CollectionsANU Research Publications
Date published: 2018-04
Type: Journal article
Source: Journal of Combinatorial Theory Series A
DOI: 10.1016/j.jcta.2017.11.020


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