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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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