We use super –Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of –modules (and, more generally, –modules) whose objects are tensor generated by exterior and symmetric powers of the vector representations. As an application, we give a representation-theoretic explanation and a diagrammatic version of a known symmetry of colored HOMFLY–PT polynomials.
"Super $q$–Howe duality and web categories." Algebr. Geom. Topol. 17 (6) 3703 - 3749, 2017. https://doi.org/10.2140/agt.2017.17.3703