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Super $q$-Howe duality and web categories (1504.05069v3)
Published 20 Apr 2015 in math.QA, math.GT, and math.RT
Abstract: We use super $q$-Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of $\mathfrak{gl}N$-modules (and, more generally, $\mathfrak{gl}{N|M}$-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.