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Super $q$-Howe duality and web categories

· 2015 · math.QA · arXiv 1504.05069

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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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On a symplectic quantum Howe duality

math.RT · 2023-03-07 · unverdicted · novelty 7.0

Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.

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  • On a symplectic quantum Howe duality math.RT · 2023-03-07 · unverdicted · none · ref 45 · internal anchor

    Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.