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Super $$q$$-Howe duality and web categories. (English) Zbl 1422.57030
Summary: 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 tensors 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.

MSC:
 57M25 Knots and links in the $$3$$-sphere (MSC2010) 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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