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arXiv · 1504.05069

Super $q$-Howe duality and web categories

Daniel Tubbenhauer·Pedro Vaz·Paul Wedrich
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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.

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Daniel Tubbenhauer, Pedro Vaz, Paul Wedrich. 2015-04-20. Super $q$-Howe duality and web categories. https://doi.org/10.2140/agt.2017.17.3703

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